Loophole-free Bell Inequality Violation with Superconducting Circuits
The talk was recorded on 13 June 2023 as part of the MCQST Distinguished Lecturer series, where Prof. Wallraff offered a colloquium talk at @maxplanckquantum.
View inside a section of the 30-metre-long quantum connection. Several layers of copper shielding circled around each other. © ETH Zurich / D. Winkler
Superposition, entanglement, and non-locality constitute fundamental features of quantum physics. Remarkably, the fact that quantum physics does not follow the principle of locality can be experimentally demonstrated in Bell tests performed on pairs of spatially separated, entangled quantum systems. While Bell tests were explored over the past 50 years, only relatively recently experiments free of so-called loopholes succeeded. Here, we demonstrate a loophole-free violation of Bell’s inequality with superconducting circuits. To evaluate a CHSH-type Bell inequality, we deterministically entangle a pair of qubits and perform fast, and high-fidelity measurements along randomly chosen bases on the qubits connected through a cryogenic link spanning 30 meters. Evaluating more than one million experimental trials, we find an average S-value of 2.0747 ± 0.0033, violating Bell’s inequality by more than 22 standard deviations [1]. Our work demonstrates that non-locality is a viable new resource in quantum information technology realized with superconducting circuits with applications in quantum communication, quantum computing and fundamental physics.
[1] S. Storz et al., Nature 617, 265–270 (2023)
Work done in collaboration with Simon Storz, Josua Schaer, Anatoly Kulikov, Paul Magnard, Philipp Kurpiers, Janis Luetolf, Theo Walter, Adrian Copetudo, Kevin Reuer, Abdulkadir Akin, Jean-Claude Besse, Mihai Gabureac, Graham J. Norris, Andres Rosario, Ferran Martin, Jose Martinez, Waldimar Amaya, Morgan W. Mitchell, Carlos Abellan, Jean-Daniel Bancal, Nicolas Sangouard, Baptiste Royer, Alexandre Blais, and Andreas Wallraff
About Prof. Andreas Wallraff
Since January 2012 Andreas Wallraff is a Full Professor for Solid State Physics in the Department of Physics at ETH Zurich. He joined the department in January 2006 as a Tenure Track Assistant Professor and was promoted to Associate Professor in January 2010. Previously, he has obtained degrees in physics from Imperial College of Science and Technology, London, U.K., Rheinisch Westfälische Technische Hochschule (RWTH) Aachen, Germany and did research towards his Masters degree at the Research Center Jülich, Germany. During his doctoral research he investigated the quantum dynamics of vortices in superconductors and observed for the first time the tunneling and energy level quantization of an individual vortex for which he obtained a PhD degree in physics from the University of Erlangen-Nuremberg. During the four years he spent as a research scientist at Yale University in New Haven, CT, USA he performed experiments in which the coherent interaction of a single photon with a single quantum electronic circuit was observed for the first time. His research is focused on the experimental investigation of quantum effects in superconducting electronic circuits for performing fundamental quantum optics experiments and for applications in quantum information processing. His group at ETH Zurich engages in research on micro and nano-electronics, also on hybrid quantum systems combining superconducting electronic circuits with semiconductor quantum dots, making use of fast and sensitive microwave techniques at ultra-low temperatures.
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You very much um for for the nice introduction and for the for the kind invitation here there’s also still seats in front so maybe around door there’s one and probably one of you could also use my seat which I’ll likely not use during this talk um yeah so so thank you very much
It’s a it’s a it’s a great honor to be here for this colloquium and and also of course to to have been chosen for this distinguished lecturer um award from the McQ uh and and it’s a a great pleasure to to visit Munich and and a really very
Vibrant Community on Quantum Science and Technology here um so so in this presentation today uh I’ll talk about the uh lopho free violation of a bell inequality performed with u super conducting U Quantum bits or superc conducting Quantum electronic circuits and uh yeah this is an experiment that we actually started
Thinking about more than 10 years ago when there were no other loophole free violations of of bell inequalities in experimental systems yet and maybe one of the biggest challenges in in this particular Endeavor was to to try to do experiments with super conducting circuits in a in a space likee separated
Fashion for having a um a bell inequality experiment done that closes the locality loophole you somehow need to achieve physical separation between superconducting cubits and the question is how to make that happen and a and a key ingredient for doing such an experiment you you see on this on this
Title slide um so the structure that you see here is is essentially a vacuum can with a set of radiation Shields made made from copper and an aluminum wave guide that is in the in the center of the structure and the whole diameter of this vacuum tube is is maybe like this
So uh and and one of my Theory colleagues rato Rena at at eth Zurich said that that he probably thought that this was the most expensive coxial cable that he has ever seen which which might be right um so what we’ve then done what
You see here is kind of a section of a of a cry stat of a cryogenic link that you can set up between two rather conventional uh um cryogenic systems between two delution refrigerators and and some sense you can think about this as a as an uion refrigerator turned on
Its side and then covering a spatial distance so what this then looks like in in our lab is is something like this uh so on the previous slide you’ve looked at a at a section um of this vacuum system with a radiation shield and a and
A microwave wave guide in the center and at one end of U this this link there’s a a dilution refrigerator which can cool electronic circuits to few tens of Melvin above the absolute zero of temperature and and if you would look into the other direction and later I’ll
Show you some more pictures and also a little video you’ll you’ll see another C that that is connected through this cold Quantum link over across a distance of about of about 30 m and this distance of about 30 m that that gives us um roughly
100 NS to do a um a bell in equality experiment that that actually manages to close the locality loophole yeah so the the experiment was was done um at at eth Zurich and a large part of it was uh really led by a a set of graduate students uh who who started
This um now close to 10 years ago actually or we started thinking about this experiment close to 10 years ago and we also collaborated on this from the from the theoretical side with batist and alexand B from the University of of sherbrook and also bonal and nicolasa at the University
Paris and we had a as you see this this looks a little bit like a partical physics experiment or you have like a big tube that goes through some long hallway and and that maybe also takes some technical effort and we’ve really really benefited a lot from from a a
Group of technicians and and Engineers that worked in our lab over the period of this this experiment and we’ve also um collaborated with the a group at IO in Barcelona and also a startup from IO qite that created a a random number generator that played an essential role
In our loophole free Bell inequality violation with with super conducting circuits and and this project was essentially started through an ERC um Advanced Grant or that that kicked off this project and uh yeah if any of you are are well connected on the political scene in Europe I I think I can’t miss
Out on mentioning to you that that currently Switzerland is to a large degree excluded from the research program Horizon Europe and that also excludes Swiss researchers from from ERC grants which is really a major pity and and I think it’s mostly a political issue between sort of the Swiss
Government and and the EU where some pressure is is being exerted to uh and and Science and education is used in in that context which is probably not a good idea which many of you would likely agree to Um so beyond the people who were listed on my title slide who who did the experimen I I also grateful to to everyone who um contributed to the progress in our lab um since 2006 when we started working at eth yeah and you see what what former group
Members are now now doing so quite a few of them are are faculty members at various institutions and also quite a number is is working in sort of an Quantum related industry in in one form or the other and and so we had very successful projects with with everyone
Here and obviously also with collaborators at at eth and and elsewhere okay so so we set out to do a bell test with with superconducting circuits and and one of the basic motivations there of course always was uh is is to just think about this question um why quantum mechanics does
Not follow the the principle of local causality so if you if you take two Quantum systems and entangle them with each other and then physically separate these Quantum systems from each other and perform for measurements on those you will observe correlations between the measurement out comes of the measurements performed on these two
Distant Quantum systems that that display correlations that um that seems strange if you believe in local causality or local realism namely the idea that physical objects carry all the information about potential measurement outcomes that can be uh found when you perform measurements on a on a physical system locally and quantum mechanics um
Violates this this principle of of local causality or local realism and and this was something that uh that in the beginning of the last century or in the in the around the 1930s yeah the inventors of of quantum mechanics were bothered by this feature and and for
That reason they they thought that maybe quantum mechanics is sort of an incomplete theory that there’s something missing in quantum mechanics that that would actually be possible to EXP explain um these correlations while obeying local causality or local realism and this was largely a a sort of a theoretical exercise or theoretical uh
Discussion during those days until um Bell then in 1964 he actually proposed an experiment and he he devised a theory that would actually enable um experimentalists then to to distinguish in in experimental work whether local realistic theories could explain the measurement outcomes or or whether the prescriptions of Quanto
Mechanics would actually need to be used literally to to predict the outcomes of measurements on entangled particles and so Belle really uh enabled like moving this question from from sort of a philosophical uh question into an experimental one and that was in 1964 and so so it’s interesting to to
Perform Bell tests for for that reason and and obviously this has motivated a lot of research in Quantum Science and Technology yeah through through a a period in excess of of 50 years but doing Bell tests is not only fundamentally interesting but non-locality can also be an important
Resource um it can be used in for example the device independent Quantum information processing it can be used for independently verifying that Quantum devices and networks actually work as advertised it can be used for uh secure Quantum communication also in the in the context of device independent Quantum
Key distribution for example and there’s applications of bell tests making use of nonlocality so Bel test which close all the accessible Loop post poles to to produce certified random bits for example so it’s not only of fundamental interest but uh using nonlocality as a resource in in Quantum information uh
Processing systems is a is an an interesting Endeavor so how does a bell test proceed so Bell test is performed typically between um two parties having access to a um two Quantum objects that can be entangled with each other and and here on the right hand side there’s sort of a
A very basic schematic picture of what something like this could look like so there’s two parties which are uh spatially separated from each other and they both have access to to some Quantum system and in our case that Quantum system is not a photon or an atom or an
Ion but it’s a superc conducting electronic circuit so in a bell test um as a First Steps step the two parties preparing entangled State between these spatially separated locations an entangled State between a cubit a and a cubit B and here’s an example of such a maximally
Entangled state so that’s sort of step one and you make use of this this entangled State as a resource in a in a bell test and then in the second step of the experiment the experimentor actually um randomly selects local measurement bases um both at the site a
Where he holds um one of the quantum bits and at side B where he holds the other Quantum bit and the random choices between two measurement bases actually locally choose um two orthogonal measurement bases that are indicated up here as as two orthogonal axes a and a
Prime at the location of Cubit A and B and B Prime which are also orthogonal to each other at the location of of Cubit B and the two two locations at which you choose these random bases um should be space like separated from each other and then to finalize the Bell protocol you
Read out the state of the cubits um in this uh randomly chosen measurement basis and and you essentially project the cubits in into these uh local igen States and you find results plus or minus one at each one of the cubits and then to to perform this experiment systematically you repeat it
A large number of times and you calculate a specific quantity namely a a form of a bell inequality and the type of bell inequality that we are using in our experiments are are the ones that have been devised by clauser horn Shimon and Hal and and John clauser was one of the
First um scientists who who did a bell test um in um the early’ 70s and the inequality equality that we use to evaluate this or to determine whether our system violates a bell type inequalities is the following one that is written down here so what you do is
You take these measurement outcomes X and Y that that reflect the the measured values of the two cubits at sites A and B and conditioned on the random measurement basis choice at for Cubit a and the random measurement basis choice at Cubit B you calculate this expectation value here and clausa Horn
Shimon and H have then constructed this um this this quantity here that you just determine by essentially figuring out which random bases you had selected and calculating these expectation values here and sort of what what bell had then been able to show was if the properties of these Quantum systems are governed by
Any local realistic model then this local realistic model would essentially Force this s value when it’s measured to be smaller than than two and if this measurement would result in this s value uh be larger than two then you would know that the physics of that object can’t be described by any local
Realistic model at all and the conclusion of that would be that that quantum mechanics would need to be Tak literally uh to to prescribe the the outcomes of such a measurement and therefore qu mechanics has this this non-local feature to it that creates very strong correlations that are not
Possible in in classic in In classical systems and so therefore it can be um um yeah you can negate this idea that there could be a alternative Theory to to quantum mechanics that that could obey local causality and so therefore one sets out in these spell test type experiments to
Measure these uh um s values and verify whether they whether you find an S value which is larger or smaller than two okay and so first experiments on that were were done um sort of reasonably shortly after this idea of violating bels inequality was phrased in in 16
Before but these early experiments they left a few loopholes open or they required some assumptions which were um then used to to challenge the conclusions of of bell inequality type measurements and one of these assumptions is the is the the so-called or one of the corresponding loopholes is
The so-called locality loophole so if you would perform measurements of of entangled particles if they’re not space like SE separated you could make up models in which some physical interaction between the two particles would would lead to the correlations That You observe and when you able to
Separate these two particles um by a space like distance yeah and and perform your measurements fast enough you can exclude that any um physical mechanisms would actually any physical mechanism could possibly lead to those correlations so that’s the locality loophole another challenge in early experiments was uh the so-called detection loophole
And that related to the fact that early experiments that were performed with photons typically measured only a small fraction of the entangled photons that were actually generated and in that case it could actually be that that the photons that you weren’t able to access in your measurement that did go undetected
Because your detection efficiency was not sufficient or or your detectors would would just not have a high enough Quantum efficiency those could in principle then obey some different type of Statistics or some different type of physics which is maybe not so likely but which you couldn’t exclude in such
Experiments and so therefore those experiments required to to make this Fair sampling assumption that all the exper all the photons that you actually measured would actually be a a representative instance of the experiment that you were actually trying to do and therefore it’s important to
Try to detect as many of the outcomes of this experiment as possible and and doing that um relates to closing the so-called detection loophole and then there’s a um a third aspect also about this which is the so-called Freedom of Choice loophole or the measurement Independence loophole
And and that requires to to choose the measurement basis here at the beginning of this um experiment um randomly and and if you if you wouldn’t choose this measurement basis randomly you you could think that that sort of some prior knowledge about this measurement basis Choice could affect um
The measurement outcomes and in fact that’s one of the loopholes that is sort of maybe even on principal matters impossible um to close because you could in principle in some super deterministic models you could not exclude that everything in the world is actually predetermined um um by U by some prior
Facts and and in Bell test experiments you try to exclude that as good as you can by by choosing these measurement bases here randomly and we tried in our experiment to address all these these Poes okay so so bsts are are clearly not a not a new thing the the they have
Been proposed in 1964 and then eight years later there were first experiments by freatman en closer that were successful in in violating the Bell inequality showing showing that this s value can be larger than two but those uh experiments had had loopholes this for early experiment had essentially all the three loopholes
That I uh that i’ mentioned and then another 10 years later there were set of of uh of new experiments performed by Alan as where he actually chose these measurement bases randomly but still those experiments left um um some of the other loopholes open and it it then took really um many years
Still until all the loops that I’ve mentioned uh were actually closed in a single experiment and if you see here the first experiments took essentially eight years from be after the uh discussion of the Bell inequality by Bell in 1964 and then it took another 10
Years but to the first experiments uh by by Anna ASP and uh um and then even a bit more time until experiments existed that successfully closed um all the loopholes and uh and some of these experiments even some some members of this audience were involved in so
Andreas was involved in in an experiment at Del uh performed with EnV centers and there’s also experiments that were done in har Vine F’s lab that that did such loophole free experiments with with atomic systems and in in 2012 um at eth like 40 years after the first first experiments
By John clauser um and before all the loopholes were closed in any other experiments we we thought about okay would it be thinkable to do a loophole free test of bell inequalities with with superconducting circuits so we made this proposal to the ERC in in in 2012 with
The with the hope that we could maybe cross the finish line still before uh before maybe the other experiments after having waited for like 40 years uh um after the first experiments and maybe for 48 years after the this concept of bell inequality violation was formulated
By by John Bell but then of course like then in 2015 17 and 18 the the experiments that I just mentioned were were performed um but we decided okay that we we would still continue to go for it uh first because it’s sort of super conducting circuits are a
Different physical system to do a bell test with in the mid 80s it was not even whether superconducting electronic circuits should obey the laws of quantum mechanics at all there were early experiments for example performed by by Michelle Devore and John Martinez and John Clark at Berkeley where the
Question was could one observe effects like energy level quantization or tunneling in superconducting circuits so a superc conducting circuit is sort of a a macroscopic Quantum system where the quantum mechanics of it are governed by some macroscopic variables like the the phase of a the condensate of uh
Superconducting charge carriers in in a superconducting electrode and and also at this time in 2012 it was already clear that that superconducting circuits would be a good system to to build quantum computers out of and so we thought that this combination of trying to um violate bels inequalities and get access to this
Feature of of nonlocality in the context of of a system that could also perform Quantum comput uh comput would be very interesting all right so so what are the requirements for a successful experiment on violating belt inequality with superconducting circuits you need to be able to create high fality entanglement
Between the two superconducting cubits uh you need to be able to perform a high fidelity readout of the cubits at the end of the experiment you need to realize this measurement independence by choosing the measurement bases uh randomly at the beginning of each belt test and you would need to be able to
Close the detection uh loophole by by measuring all of the outcomes of the experiment which is probably the easiest loophole to close in super conducting cubid systems because essentially there’s there’s High Fidelity readout and since the cubits are stationary they don’t go anywhere so you don’t miss them
Uh and and as long as you can create high or realize High Fidelity readout that was one of the easier to close loopholes and as I alluded to in the beginning already closing this locality loop hole is maybe the most challenging aspect and so at the time when we
Devised the experiment um we we tried to estimate you how much distance we would need to realize a space likee separation between the cubits at site a and the cubits at site B and here in these colored cones you see two uh two light cones essentially extending from the SpaceTime location
Where you do your measurement basis choice in the in the beginning and uh that and those light cones should hopefully not intersect with a space uh time location at which the the measurement of your individual cubits is finished and so to estimate how much physical separation we would actually
Need we we figured out how long a high fidelity readout would take and we estimated that that would take 50 NCS um roughly and we’ve developed the technology that was required to to achieve these short readout times then for this random basis choice we use technology that was U developed by this
Spanish startup company um Hite that spun out of IO whose random number generators were also used in the three other loophole free Bell test like at Del um at uh in Anton singers lab in in Vienna and also in the in the nist lab in Boulder so and these random number generators
They take about 30 Nan seconds to create that random number and then to turn that random or that random basis choice and turn it into into turned measurement bases at one of the superconducting cubits and then in this experiment there’s also sort of some distances that signals travel from the random number
Generators to the cubits and then the readout signals travel from from the cubits and their readout Electronics themselves into the detection electronics and so we figured that we would maybe need 100 nanocs to perform this experiment and that would then translate into requiring a physical separation of of 30 Metter between the
Two cubits uh at the sites A and B of your experimental setup and and I should maybe also mention that when we wrote this uh proposal up initially we thought that 10 Metter would be sufficient to do to do this experiment and one of the reasons for that was because at that
Time there were really uh no loophole free experiments around yet and none of them really used this measurement Independence Criterion where you need to pick measurements at random through a physical mechanism that would create this Randomness and that added sort of 30 Metter to our time budget and that
Required us to make our experiment 10 meters longer which was not good news yeah because that would just make the make it a an even bigger effort and then we were also maybe not quite as fast as we thought in our measurement and and and maybe we didn’t
Account fully for the for the for the propagation times for our signals initially uh so so we set out building a 10 meter system um but in the end we ended up needing to to build a 30 meter one okay so so what are the requirements for the initial entanglement that you
Need to create uh in for this Bell experiment and for the readout of the super conducting cubits and and and one of those special aspects about it is maybe that that we can use this entanglement as a resource we we sort of create the entanglement up front in the
Experiment before the actual Bell test starts yeah so we create an entangled pair and that only then is it that we choose the random measurement bases and then we perform the measurement so the entanglement generation essentially doesn’t figure in our Criterion on closing the locality loophole but nevertheless we need to
Make sure that that the Fidelity of the Tangled state is high enough and the readout Fidelity is high enough so that we would be able to create s values which are larger than two and here on the right hand side you see a plot uh in which readout Fidelity is plotted versus
The concurrence of the intangle two Cubit state that we create and and there’s these lines plotted in this the spot and if you’re to the right and above this line you would be able to achieve a violation of of the S value by the amount that is indicated
And at the time that we devised our experiment we had already demonstrated to ourself that that we could entangle um two cubits even on two different physical chips with concurrences uh in in the range of of maybe um 77 or so corresponding to fidelities of maybe about
80% and and so that would uh leave us along along this line here and that would then require that we would need to realize single Cubit readout fidelities in in excess of maybe 96% or so which is quite challenging to do even on small time scales okay and and we actually did go
Ahead and devis these Technologies to perform very fast single Cubit readout with High Fidelity and actually in in 2017 we were able to demonstrate 50 nond long single shot readout with a Fidelity in excess of of 98% and this still today is is one of the best Cubit readout that exists and
And our motivation to develop it was really to do fast readout to enable this experiment um at that time most of the readouts would take maybe several hundreds of nanoseconds some people who had cubits with with long enough lifetimes would even integrate for 500
NS or so but for us it was clear that we didn’t want to build a system that was maybe 150 M long or even longer so we had a really big motivation to make our readout really fast and and interestingly what that has led to is it really forced us to develop
This fast and High Fidelity readout that then helped us later in all sorts of other ways for example in our Quantum error correction experiments where it’s extremely important to perform fast and High Fidelity readout in the middle of executing Quantum circuits in an arrow correction cycle and and this we’ve essentially
Developed we’ve made use of this technology developed in 2017 for this particular experiment in our one of error correction experiments okay so so how to address this maybe most difficult to address a loophole this locality loophole with superc conducting circuits and I’ve given it away already in the discussion
Of of my my title slides and so when we when we designed this experiment we we thought okay what do you want when you when you want to connect two super conducting circuits in two different cry steps for example you could think about converting microwave frequency excitations into Optical frequency
Excitations and then send that Optical frequency excitation through an optical fire to fiber to the other cep and then do the same in reverse and establish entanglement in this way and there’s a a large body of research and ongoing experimental effort that tries to do high Quantum efficiencies um converters
Between microwave frequency uh photons and Optical photons and in principle you could imagine establishing entanglement between two superconducting cubits that are remote from each other in this way but still today the Fidelity at which these converters uh operate are not good enough to create entanglement that would
Be able to violate the bell in equality so we decided that we wanted to build a link that operates at microwave frequencies because we essentially knew that that all the interactions that we mediate between superconducting cubits on chips for for doing gates for running quantum computers they would work at
Microwave frequencies by coupling cubits between through microwave frequency wave guides and if we could somehow make it just a very long microwave frequency wave guide we were pretty confident that we could be implementing all the interactions that would be required to to do this also in a non-local fashion
And use essentially existing Gates and protocols for doing so and so we thought a little bit for a moment about how cold maybe this link would be and and we figured okay if it was as cold as the wave guide on a chip that we would certainly be safe and so
We decided to go for that and one of the studies that we did at the time also in around 2017 we’ve actually looked at different waveguide Technologies like coio cables or three-dimensional Hollow wave guides um and and measured their loss and sort of one of the interesting
Aspects is that the loss in such a superc conducting wave guide can be less than a B per kilometer so it’s about as good as the loss in in a good Optical frequency fiber and therefore we we were quite confident that we could connect systems remotely with each other and if
It was cold enough then thermal background radiation would also not matter even though that for example P Sola and also pel um um have thought about how you maybe run entanglement protocols between two remote superconducting cubits in the presence of a little bit of thermal background
Radiation in this wave guide and so what we also wanted is we wanted that experiment to still be doable it should end up with a cryogenic system that actually cools down on some finite time scale without you waiting months or so for for doing that and and we wanted a solution that
Is maybe modular and and in principle extensible in some form and so what we came up then with is to to just look at a conventional cry step which is shown here which is has essentially a vacuum can and then different Shields at diff which are held at different at a set of
Different temperatures so there’s a 50 Kelvin Shield a 4K Shield a still Shield that is kept at about 1 Kelvin and a base temperature Shield that is typically kept at a few tens of millin and then inside that base temperature Shield you would house everything that
You would care to keep cold and our our thinking then was okay let’s just take this thing and turn it on its side and see how long we can extend it and and so here there’s this cross-section of of the system that I’ve shown to you already on my title slide which
Essentially inherits the same components the vacuum can and the different radiation Shields and a wave guide in its Center yeah and and this is essentially what the thing that we then constructed looks like and um now what we’ve then then built is is this this lab where you have
This type of wave guide technology with uh two cry stats 30 m apart from each other connected by by this long line and and so I have a little video so I invite you all to to come and take a look at it it’s it’s sort of an an impressive setup
So everyone who has seen it sort of I think liked the experience and so now here you get the uh the video version of that um and so you you see there’s the you start looking at the at the first C and there was a little bit of audio with
It but okay that doesn’t play now so one of the special features of the cry is that it also has a site access so we can pull out cables to the side so that we don’t lose the the distance in the space like separation in comparison to to
Pulling out the cables to the top which is the standard thing that you would do in C stats and so now in in in this video here I just walked along with my iPhone and recorded the video and there’s a so this there’s a central cooler here in the middle that is 15
Meters away from the first C that that houses one of the cubits and that keeps some of the thermal radiation under control and then there is another 15 M um to the to the next priorat and essentially this this link is uh is put together from these two and a half meter
Long sections of of structure that you’ve you’ve seen on on the title slide and essentially you can now use this this wave guide to start uh the Bell test experiment by uh or to prepare the resource for this Bell test experiment by entangling two cubits over
The distance of of 30 m and then you have local control electronics at each side that you’re trying to to to face synchronize to be able to to measure the phase coherence of the entangled states that you that you establish and so here this is a it it it
Looks like a a small mockup but it’s actually the the cat drawing of the whole system and yeah there’s this this 30 meter long physical system that includes one and a half ton of copper radiation Shields and and about 14 th000 screws to to assemble this to cross uh
These these 30 MERS and and to even get this designed and manufactured and then and then put together is is sort of a major effort and and and it indeed looks a little bit like a like a particle physics experiment okay so so how well does this work from the cryogenics perspective so
Here’s some so on every section so there’s a there’s about 10 sections in this long link and it test temperature sensors at every one of these blue points and so we can we can measure the temperature profile of this whole system and at the coolers at at both ends the
Temperatures are the ones that that you know from regular dilution refrigerators so they’re about the outermost Shield is at about 50 Kelvin and the physical performance is then limited by essentially some balance between the thermal radiation that impinges on this outermost radiation shield and the thermal conductivity towards the cooler
And that sets up these these temperature profiles that you see here and indeed the the biggest challenge is to deal with the black body radiation from room temperature and therefore at this 30 m distance you require this intermediate cooler at at at uh after about 15 M that
Cools the outer two most Shields but not the inner Shields and so you can look at the temperature distribution for this 4 Kelvin shield and there you see that the gradients are already quite small and then there’s this one Kelvin or still Shield and then there’s the base
Temperature shield and so one of the interesting things is now you have this pretty gigantic cry stats and still in the middle the the hottest point is about 50 Melvin above the absolute zero of temperature cooled only by these triats at at the two ends and to cool down um this whole
Apparatus takes about seven days and and the interesting bit of it about it is that that six and a half of those days are really uh used to cool against the black body radiation and get everything to 4 Kelvin and then it takes maybe
Another half a day to get it to to the lowest temperature that you do experiments with and U so this we did not do in one step but we we did build a set of smaller systems initially with a 5 meter separation and then one with a 10 meter
Separation and and on the 5 meter one we we had a publication in 2020 okay so um so how does it go now to do this uh this Bell test so here’s this the schematic with the two c stats 30 m apart from each other and you really
Start out with entangling the two cubits with each other and uh um this is a deterministic uh generation of remote entanglement and and this we demonstrated with with two super conducting chips in a single cryosat in in 2018 and and the protocol that we used this is actually some that was proposed
By by nasio and collaborators uh yeah in 1997 were we essentially um emit time reversal symmetric photons from from one of the cubits and then with high efficiency reabsorb them at at the other Cubit to both perform quum State transfer and to create entanglement between the remote
Cubits and in these experiments we can then create a bell States between the cubits living in the two cats at the end of this cryogenic link and for this 30 m system that you see here we achieved a a bell State Fidelity of about 80% between the mo remote
Cubits and and the main source of infidelity here is is the loss and it’s not the loss of the 30 meter long wave guide but it’s it’s rather the loss that connects um the cubits on the chip to the input Port of these wave guide and and these these connections are
Currently still made from from normal metals and the PC boards which are involved are are made from normal metal and they have a little bit of loss so I’ll say a few more words about this this entanglement generation protocol you essentially start out with preparing the first cubit in its first
Excited state with a pi pulse and then apply a pi half pulse to create a superposition between the first and the second excited state of our cubits so these superconducting cubits have a have a set of excited states that you can make use of and then we use a um um a driven
We use a drive to uh to map the excitation from the Cubit into a photon um that can be stored in a resonator that is coupled to the Cubit and then the photon will leak out from that resonator into a wave guide propagate along the wave guide and since the
Photon has a Time reversal symmetric shape or at least the shape that allows for the high efficiency reabsorption at the remote side we can then have that Photon travel to the Cubit 30 m away and absorb it there and in this way transfer excitations and also create
Entanglement and at the end you can go ahead and and just characterize this this non-local Bell State by performing um um tomography on this two Cubit system and so maybe I say a couple of more words about it yeah so this is also inspired Yeah by by ignasio uh proposal
But also by work that done in gadus lab so one way to look at that in our setup is we have this three-level system it’s coupled to two crossed cavities one of the cavities we use to have the Cubit emit a photon into that cavity the other
Cavity we can use actually to perform this High Fidelity read out of the Cubit State and we have essentially a symmetric system on the other side again a cubit with three levels and a cross cavity and then there’s this uh um this unidirectional wave guide that couples
The two systems um to each other and what we actually use is we we make use of the second Cubit excited state which we label F here and have a microwave driven transition that couples the state with the Cubit being in the second excited state and no Photon in the in
This Photon emission cavity shown here in yellow to a state where the Cubit gets transferred to the ground state but a photon gets created in this in this Photon emission cavity and a photon emission cavity then has a large coupling to the wave guide so as soon as
There is any Photon component in this cavity it will leak into this wave guide and start to propagate towards the other cubid and at the other cubid we can essentially reverse that pulse here and at the other cubid the the the pulse will absorb the photon from then this
Absorption cavity here and transfer it to the Cubit to create a cubit excitation and and and this works with high efficiency if you can make these Photon shapes enally time reversible and this we demonstrated in this 2018 paper for the first time and at the time maybe it was obvious to some
That one could do Bell tests with it but but we didn’t discuss it in that context um so what we chose for the for the photon shape is to take this uh cosine hyperbolic shape here and actually in experiments we could extract the photon from the wave guide and just
Explicitly verify that we have this time reversal symm shape of the photons that we create and this is discussed in in a in the set of papers here where we thought about it a little bit initially and and then uh worked on the calibration of that and then there was
This nature paper that that discussed the use of of this protocol to transfer States and to create remote Entanglement okay and then there’s a few details about calibrating this this properly and one of the critical things to to make this work well or one the analysis methods that we’ve used is we we can perform three level readout of our cubits and we can hold this this
Transfer pulse that was labeled G of T tilder we can stop it at any given time and and read out the excited state population of or Cubit both in the second excited state and the first excited state and the ground state and this is a very good indicator whether
This transfer protocol actually works because as the Cubit goes from the excited state to the ground state as this pulse length is increased and calibrated properly you see the ground state population um go to Unity and you would try to avoid to populate the first excited state of the cubid and and this
We could verify in this way um in our experiments and since we have an isolator in our wave guide we can extract the photon from this wave guide and and physically look at it and and so here is a picture of the envelope of that Photon and to be able to measure
That envelope of a photon rather than emitting a photon in the wave guide we have superimposed this this photon with a vacuum State and made a coherent state of zero of the zero and one Photon Fox State and then measured its average amplitude and and we can understand the
Average amplitude and the and the black solid lines that you see both on the left and and the one that disappears behind the data here they come from Master equation simulations that that that that model the physics of this of these interactions and this shows that we can understand really the details of
It okay so so this is the the technique that we used to create this entanglement additionally at the Fidelity of 80% corresponding this to this concurrence of of about um um8 or so and so then this is a resource at the start of the Bell test but then the actual Bell test
Starts with choosing our measurement bases randomly and these random number generators of this company qite that was founded out of EO they take about 17 NCS from the moment that the physical process starts that creates the random number to the random number generator create a trigger signal as its output
That we can use to then select the cubic measurement basis and so so this is the moment in time that then uh creates our our light cones for this picture here and uh this the the random outcomes of this of this box zero and one they’re used at at
Either side to pick the measurement bases b or B Prime and a or a prime and then in every Bell inquality experiment you can turn the measurement bases at the at the two sides relative to each other by this control angle Theta and and when you look at Bell test
Experiments usually you see this s value or the S parameter plotted against this control angle Theta and for some optimal value of theta the um the Val inequality is typically violated um so then the signal propagates from this random number generator to our Cubit and the Cubit basis rotation pulse takes about 12
NS and then we perform uh so and this basis rotation pulse is essentially a pi half pulse of of the specified operations and then the the next big step is to perform the readout in single shot of the Cubit and this readout we decided to to perform for 50 NCS and in
This 50 NCS we achieve a certain Fidelity and if we would integrate for longer we would increase the Fidelity and if we would integrate for for a smaller time we would reduce the Fidelity and and this was something that we’ve demonstrated in this 20 2017 paper which I i’ mentioned
Before um and then finally there’s a little bit of signal propagation delay um of of the readout signal towards our ADC which then digitizes that we out signal and uh and with that digitized read out signal we can then assine this assign the measurement outcome of that
Particular Cubit and and when it’s in the ground state we assign it an x value of plus one and an excited state an x value of minus one and then we repeat the measurement a million times and we um according to the protocol that I’ve just described to you a little while ago
We calculate this s value and we do so um for uh a set of measurement angles between the two basis sets at the two sides which is par parameterized by this angle Theta and so yeah here’s the result of that that measurement um so in this
First plot here what you see is the the expectation value of the measurement outcomes of Cubit a and Cubit B which are called X and Y and they’re calculated for the four different combinations of measurement bases choices or there’s a and a prime and B and B Prime and there’s four different
Combinations you could have a and b and a and b Prime and and a prime and B Prime and uh um and and the one that uh that I’ve not said yet and so what you see here is is how these correlators vary in dependence of this control angle Theta so you see
Sinusoidal oscillations and the sinal oscillations ideally they would reach from from minus one to one and since both the readout Fidelity is final and the initial b State Fidelity is final the contrast is slightly reduced from one and based on these expectation values you then can can calculate this s
Value for the Bell inequality violation and here this s value is is plotted against this angle Theta between the two measurement bases choices that we control and in any Bell experiment uh there the Bell inequality is only violated in regions about the appropriately chosen measurement bases uh
Angles and um so here already in this in this experiment in this initial data you see that that uh apparently s um um gets larger than two by by a little bit and uh so first we have compared that to what we would expect how large our Bell
Violation as should be based on the coherence properties of our system and the red fidelity which we can then stick into a master equation simulation and we find good agreement and what we’ve then done so so this here for this first data set this has about a million repetitions of this
Experiment and they’re distributed over these n angles that we chose to measure and then we did three more experiments around the two specific angles where the Bell inequality seems to be violated strongest and and we’ve performed a few additional measurements distrib a million uh measurement points across
This set of measurement angles and we clearly see that around the angle of theta of minus Pi quter we see a significant violation of the Bell inequality and also about the angle of plus 3/4 PI we see a a significant violation of the Bell inequality in this
Data and then to wrap this up we picked a specific point where the B inequality appeared to be maximally violated and we repeated the experiment there for a million times s and our average s value there that was recorded is 2.07 um so that 2.07 is is is a little
Bit above two so not a lot above two but because we were able to do in about a half hour experimental data we were able to create collect about a million repetitions of this experiment uh we could create a very small eror bar on this data set so the the standard
Deviation is is quoted here and this s value here violates the Bell inequality by by 22 standard deviations and and you could also calculate the P value for this type of experiment and the P value is is uh 10 to the minus 108 or so so that P value
Is is maybe even unreasonably small and there’s likely sort of systematic errors that that are larger than that P value but if you look at sort of initial Bell test experiments by by clauser and also by anay they they typically violated B inequality by maybe 10 standard
Deviations and um and the the loophole free B tests with photons also violated by a large number of standard deviations and this first experiment with with Envy centers had very little data they Le the first version of that experiment had only say a few hundred events where the
B inequality was violated and therefore the the P value was was not as small as one would maybe have wished for but here because the repeat rate is large um we can essentially acquire as much statistics as as we want so I think this is then beyond Reasonable Doubt um
Violating the Bell inequality with superconducting circuits so what about the loopholes so the freedom of choice loophole we we close as best as we can in the same fashion that the other experiments did with using these random number generators the detection loophole is closed by by in our experiment really
Simply taking all the measurement data there is we we measure every entangled pair that we create and and and analyze it and the locality loophole is the one that we needed to look at a bit more closely so we had this goal of of uh um of making sure that the
Experiment fulfills this this locality constraint and um and when you actually look at it the separation between the two cubits in the ch is is 30 m but what matters in light cones is is the locations of the random number generators that Define the start event in the Bell test and these
Random number generators they sit in the line of sight of this long link to the sides of the cry stats and that was also the reason why we took the cables out at the sides of the cry to to gain extra length so the real physical length that
Matters in this experiment then is is is about 33 M and as 33 M gives us a Time budget about of about 109 nanocs to to conclude the experiment and so one of the challenges was to measure that separation with with the right accuracy and so then when you look at uh
At all the details of it you see that the protocol duration in in our experiment is about 107 nond uh and the margin is about 2.8 NS and and that margin is uh holds this locality loophole with about eight standard deviations and so there’s now some
Choice that you could make you so in principle you could you could reduce the measurement time from 50 NCS to some smaller value that would reduce the Fidelity maybe reduce the the S value a little bit but but grow this timing margin yeah and so this this timing
Margin is I mean we would feel uh happier if this was now 30 NCS or so but if it was 30 if you wanted it to be 30 NCS you would you would need to to make the the link even 10 MERS longer and maybe for future versions of this
Experiment if if the initial entangled state is much better for example if you created an entangled state with maybe 95 or 98% Fidelity then you can give up on readout Fidelity and still have a large s value and giving up on readout Fidelity you can choose to integrate for
Less long time and have more timing margin um but in our paper and the supplementary material we look at the timing margins and and the violations in in all the different experiments and and sort of this is there some experiments that VI that have more safety margin on
The timing um but but some of the experiments are on a similar level so finally I want to briefly compare our experiments with with the other loophole free belt tests and and those are plotted here so there’s the Bel tests that work with um with uh with photons that are essentially create where
Entangled pairs are created in parametric down conversion processes and those experiments typically violate the Bell inequality by a small amount so if you calculate s minus 2 if you thought that maybe our 2.07 if you felt oh you wish that that was two square < tk2 and You feel that okay that was too small then all the photon experiments actually violate the B inequalities by even much smaller amounts but because these um experiments run with a high repetition rate typically they can acquire a lot of statistics and therefore even at small violation be certain that they really Violate the Bell inequality and then there's these experiments uh yeah like like the one from har Vine photos group for example and the and the Del experiments with the enry center that use meta cubits and those typically are able to violate the Bell inequality by a large margin but The experiments have have typically a much smaller repeat rate um than than the ones with uh with parametrically with phon pairs created in parametric down conversion and so our experiment comes in in a sort of an in an interest in region so it has a relatively High Repetition rate so that allows us to create a Million Bell pairs in half an hour or so easily and and now we're currently I think last weekend or so one of the posts was was trying to to run 10 to the nine Bell tests and and and see What the statistics of that would look like and these 10 to the nine Bell tests you can run say on a on a couple of days over the weekend for example so there is a high repetition rate and a and a reasonably High uh violation of the Balance in equality and if you look at what is maybe achievable is I think there's quite a bit of room to the uh um to larger violations by reducing the photon loss essentially between the the chip itself and the input of the wave guide that connects the two CS so our experiment creates high rate and high violation in in sort of an interesting region and that would also motivate us Beyond sort of just doing the spell test which is fundamentally interesting to look for applications so we could think about this device independent Quantum key distribution applications we Could look at Randomness generation using Bel tests and and different Randomness expansion protocols and there's different variants of that that that have also been addressed with other Bell test type systems but that could maybe have have particular relevance because of the high rate and the high violation that or reasonably High Violation that we get in our exper good and then and then we have this very special experimental setup and you could ask yourself what to do with it yeah there's this two cry stats connected over 30 MERS yeah so so in in in the valto mear lab there's a a system Not quite as long but which has similar features where two c stats are connected across maybe about 8 Metter or so seven or eight meters as if I remember correctly and this is pretty special um like this long version is pretty special because it can maybe used to to demonstrate device Independent protocols and can explore non-local physics in super conducting circuits but it's also an interesting waveguide QED system or you have this very long wave guide that you can now explore other physics with um um at the quantum level and uh what is also interesting and what motivated us as well to to Build the system at all and maybe even smaller versions of it is that you could think about connecting quantum computers making Quantum Computing networks um for example at the stage when when you failed to fit more cubits in your single cry you could think about what would the networking architecture look like and Maybe you wouldn't create a network over tens of meters but having C STS maybe a few meters apart from each other um to exchange Quantum information between each other could could help to extend the reach of of quantum Computing architectures and and there's also a question about about how maybe Distributed Quantum algorithms could work in in systems where where you maybe have some constraints on the on the quantum communication between different chips that can be realized okay so so I think there's maybe interesting things to do and and and if any of you have sort of some Fundamental physics ideas what one could do with with a system like that that we would of course be be very curious with and and I do think if you ask yourself okay how how big could such a system be I think we could probably relatively easily build a 100 meter version of that And if you sort of really really wanted to you could probably build an bigger version if somebody would say Hey you can detect gravity waves or or something similar um or or detect Axion in a in a in a special way yeah then then you Could do this it's maybe a bit of work and it's a I mean it's it's also not super cheap but also not not crazy expensive so so one of our students had had kind of calculated that even at our production cost it's it costs about the Same as a as a meter of highway so so depending on how expensive you think to me of highway is you could say okay you could make a system that is that is long enough U um Crossing larger distances all right so with that I'd like to thank you for for listening to Me and i' thank everyone in our lab who had had uh worked on this project and uh and and maybe you've seen this picture before from our lab and and I've never said what this really was about but this is a kind of a an old photo that was Taken really in the early days of this experiment where we essentially as one of the first components we bought one of these cry stats that had access ports from the site and if you unmount the exess port you can essentially look through your cat and that was one of our Students Paul man who's now working at at at Allison Bob this uh Quantum Computing startup in Paris and and there he figured that the alignment of of the vacuum cans was good all right thank you very much for your attention nice and I'm sure there are some questions you don't even need a Microphone I start with one from the very first beginning uh also here you talk about nonlocality as a resource um what would you say is difference to entanglement as a resource so I mean uh you need entanglement for violating the B inequality but not all entangle states will violate this so what's the Difference I mean there's there's there's not a huge number of experiments in which non locality is is a resource for example in these device independent protocols those require locality to to be able to prove the validity of some of the protocols without making any further assumptions about the devices that are Used and and on on fundamental grounds yeah you you can you can exclude some things from going one wrong if if you can perform experiments on on particles that are space likee uh separated from each other because then in the end there's no other mechanism and quantum mechanics itself that can for example Lead to correlations in in experiments that that test the Ben Bell Inequality For example or in experiments that that try to create random numbers from Ben Bell inequality type uh measurements or from Bel type correlation measurements and there's a a few a small set of of of experiments that are enabled by by Nonlocality as a resource yeah um and it's an additional resource to just entangle having entanglement available it it opens a sort of a a range of of experiments that are otherwise not possible and like for example the device independent protocols that are realized and some of those have started to be Demonstrated with uh with Optical frequency systems uh recently so what CLS the Fidelity of the preparation yeah so so I mean one of the sort of one of the challenges we saw in the beginning so so initially we had an isolator in our or or circulator in our Setup and and if you looked at the specs of this circulator um it the the circulator has some insertion loss and and that was the the component we used also to extract the photon from from the line and at the time sort of everybody seemed comfortable with blaming it on That on that circulator and then then we actually took the circulator out and and typically with these microwave components the specification are to be interpreted in a way okay this component should never be worse than this number but actually the component can be better than than the Number that is specified and actually in the frequency range that we were using that component was much better than than the specification so we took it out and it essentially made almost no difference because the loss was not actually from that that that that circulator and it's Also not a protocol dependent but it's it's in a in a good fraction it's the impedance mismatches between the ship that sits on a PC board and then the single Photon that we use to create the entanglement is transferred from the chip onto the PC board into a connector On the PC board into an adapter uh that sits on that connector on the PC board into a cable which is a normal metal cable into another connector and into a launcher that then goes into the wave in the aluminum wave gard and um maybe like Five years ago when we were sort of in the preparation of this experiment I I was trying to convince our our team of grad students that that rather than doing a chip on a PC board we should use sort of an approach like it's used at Yale where you could put such a chip into a 3D cavity and then you could bolt a chip in a 3D cavity directly to this aluminum wave guide and in this way you could exclude essentially any of the loss that that would that is present in In in our device so I think an interesting experiment would be to do that and and see how good the entangled State could actually be and and I think you could could make very high fidelity in Tangled States and of course it's always easy to to claim something and It's much harder to then demonstrate it so I do think that that we could make 95% or maybe even 98% or even higher Fidelity States in exactly this way by using the same protocol but eliminating the the loss um between the sort of the Cubit and and the input to this wave Guide because the wave guide itself has this really tiny loss of a DV per kilometer so the actual propagation loss really doesn't feature at all in in this analysis so way are you seeing some Herald by using polarization or okay so okay that's a that's an interesting aspect so We have demonstrated already so we used a Time bin encoding for the state transfer and and instead of sending States as superpositions between vacuum and and the Fon State we've we've U um sent the states as superpositions between two subsequent time bins and and in this way we we were for example to Able to create to to improve the Fidelity of the state transfer and in this way you could in the right way also improve the the entanglement Fidelity for example and you could think about other heralding type of of mechanisms but these heralding types of mechanisms they would also take more time and then It make it might make it harder to to CL close these loopholes at the at the same time preparation so this this is doesn't matter it's true okay sorry I forgot about that I explained it before but now now I I mentioned it in the wrong way so That that that indeed shouldn't matter in this in this in this context but I I think for us the the most the straightforward way is to try to eliminate some of the loss that we think comes from from this part of the connection of course you now say oh how How sure are you that that's really it and that there's not some other subtle detail that we have been taking into account and I would always as an experimentalist I would say okay it's it's maybe not so obvious until you have done the done the experiment but I think There's there's head room it's not that we're stuck at this 80% and wouldn't know what to do to improve the um the it of the intangle states which is also important if you were thinking about some distributed Quantum Computing protocol you would certainly like to have this entanglement generation Fidelity high enough to to for it to really be useful and and I think there's various things that you could do even without resorting to heralding protocols okay so so you mentioned that uh this the technology of the microwave link can be used to sort of connect different fridges right to like Scale Computing architectures uh and so how does that contrast now with say the sort of trans transduction to Optical Optical frequencies like what is I think there like realistic progress next at Optical frequencies so this doesn't this wouldn't work yet so I think if you if You even take the the best hardware that is available for this microwave to Optics transduction currently it's not good enough yeah you you you just you couldn't do this experiment having a photonic link between them and and not because the IC link would not be good but because the transduction is has sort Of either not enough Fidelity or not enough bandwidth or or too much background and and so if you look at it yeah this this this this wouldn't work and that was also the reason why we did go I mean this is sort of the conservative approach it's maybe you Could say it's a bit Brute Force yeah but but it does work yeah and and it does work reasonably well and at least shows that that you could use this sort of technology and there's also ways to to extend that you can sort of frequency Multiplex in the wave guide rather than Using this three-dimensional very bulky wave guide you could use coaxial cables and now there's better ones than five years ago then when we first time looked at it and and you could run many channels uh through such a link for example so so I think this this is an Interesting question and also in other systems for example in in rudberg atoms there's a nice paper from Misha lukin group and vadon vtic I think where they' have thought about what the constraints are on sort of connect modules to each other and and what you would require on sort of Creating interactions across sort of say some form of Link mechanisms and I think they had in mind that maybe they put RBG atoms into cavities and then they connect different patches of RBG atoms through photons that are connected via VIA cavities and so so they've done some interesting analysis for example in the Context if you were trying to run surface codes across such a link so what would be the constraints and and that's kind of interesting questions that would enable thinking about um yeah when you build very large systems how would you connect these modules to each other at at high enough quality Levels for for this cality loophole I mean you didn't want to make this much longer right so it looks like that you just outside this line light right and then I was wondering how do you measure propagation delay do you use the vacuum face velocity the face Velocity in your wave guide or no it's a vacuum it's the free space I think it's a free space velocity of light because the the phot will Trav with the group velocity yeah but that doesn't matter because in the end you you you you want to exclude all the physical mechanisms That could lead to correlations between measurements of the cubits and and what matters there is what is bounded by by space likee separation at at the speed of light in vacuum which is the worst case yeah because all the other cases where your your your information propose propagates through some medium The the the the speed of light is slower and then you have more time velocity and face velocity can be super but but in in the okay good so so then then one could could wonder about what what interactions are inter what in interactions are mediated by by the the The super luminal part of these velocities um so everything else can be um maybe ignasio has a good answer to that I I don't answer can can I mean on this on this information level I would saying then then okay how to think about sort of the physical Interaction and and sort of the information exchange I mean in a in a context of a I don't know a teleportation experiment for example and there's instances where that's um good to look at but I mean the the typical argument in this context is uh um considers the the free space velocity of Light as as as the criteria to look at in this context and and I mentioned it already yeah the margin if if you ask okay at what margin would you feel more comfortable yeah and I would also be happy if that margin was bigger but you Can trade uh violation of the S value to um to sort of uh locality uh constraints and and because you can reduce the integration time of the signal and uh and and and uh essentially give up a little bit of s value for getting a bit more um locality constraint but some of The other there are some loal free U violations of the Bell inequality which have sort of in terms of sigmas similar level of violation and also in terms of the real time a similar level of violation but there's a or of closing of this loophole but there are some Experiments which are much better than ours on on on that and um and and our lab is a little bit longer still and and we have two more two and a half meters units sort of sitting somewhere um but but we figured it wasn't worth our while at This stage to to sort of gain another few Nan seconds by by making the thing another five long we know that could I would much rather go for creating higher initial entangled States and and being faster if one wanted to be more comfortable with it but but we took a Lot of care um um with with making sure this is um well done and and there you can look at the um at the supplementary material of of the paper which which probably discusses at uh at a level of detail the the experimental aspects or so that that compares variable to to Everything else that was done in this field and and maybe also the other thing that that you need to need to look at is so so this now took some time to get get done but but essentially there was one attempt of trying to do a a loophole free Bell inquality violation with Superc conducting circuits and I think it came in uh ticking all the marks on the first try quite convincingly we find I I haven't really thought about it so maybe you can you can tell me um I mean your experiment and all the other experiment that you showed on your plot Was done with two cubits two inter tangle cubits so what happens if you go to three four five I mean is is there is there also some potential to explore something I mean there's all these other types of uh um um I mean where you can look at yeah the the predictions of Quantum mechanics versus sort of local realistic models that make use for example of of multiple of not looking at entanglement of of of two level systems but looking at entanglement of three level systems so there are some some people who think okay good why why would You bother even to do such a B test in in this kind of settings because there are slightly different settings that that you could consider um could you do things on the on on sort of on the fundamental physics level with more cubits or or is the question more if if You had more cubits on each side what would you do with that states or whatever I I think one thing that we're certainly interested in is is to have more cubits each side and and we have a project jointly also with with ignasio and and petel and and johanes fin Andar where where we ask ourselves okay if we had multiple cubits what kind of experiments could we do could we do some entanglement distillation or entanglement swapping experiments some some non-local teleportation types of experiments things that allow you to do Quantum Computing at both ends yeah this is clear but fundamental questions are You interested in um yeah I I mean I I know that there's kind of these um multi-level systems that get discussed for for testing contextuality type questions in quantum mechanics um we've we've not yet uh um thought very hard about what our next uh what the next experiments will be so the experiments That we're currently working on on come from this context of device Independence and and uh exploring Randomness with these uh loophole free belt tests so if you have a good suggestion of of of something yeah so so so we don't uh I don't have the killer application yet and and Certainly anybody has something bigger system not just with two there was also could have a a triangular Network or so yeah or or build it vertically and see whether gravity matters in some form so so it was already hard to find it so this is installed behind the parking Garage on on on the hunger compos because like finding a 30 or the actual lab is probably more like 40 m long or maybe even 45 M long but it's maybe three meters wide yeah and um your colleagues are typically not so excited when you tell them that you Need sort of space for 30 meter long experiment because that takes more or less all the space in a hallway or so maybe not on the all width but uh but sort of some technical constraints but but I think as if if the motivation is big enough um You could explore using the system maybe for some sort of long Baseline interferometry it could be interesting there's maybe some fundamental questions that have been looked at I think there's there's people who look into like Axion type of detection where they think about how they how they transport the Microwave signals that may be the photons that may be generated from sort of some detection region or from from some region in which the the photons are created and for examp example large magnetic fields to the detectors I mean that there could be interesting aspects um but we we've not I was wondering for example you asked me for proposal I was wondering for example if you have a three particle angle State you could put something in the middle so so maybe because it encloses the area you don't have an area can something happen in the area that you can find out Or something I'm just speculating said interesting single click yeah no this is clear this is clear maybe I have I have no good I've have not written up the next proposal yet so that we need to do by Fall maybe and include me in the proposal you have a good idea we'll Certain do just was curious whe whether you know what the influence of the temperature in the middle is doing to your experiment do you have the possibility to heat up the wave guide as we are doing with our cure cable to to see what happens when you transmit States for noral environment so this would also be very interesting to address these kind of P Sola and pel kind of kind of questions and in particular in in the instance where we have the isol or the circulator um in in the setup we could we could use the Circulator to also inject the thermal field so we could either you could either physically heat the cable like you did or or you could probably have a port where you inject thermal radiation into this wave guide and then see how your protocol uh works against this this Thermal radiation um in the wave guide and then you could for example explore cooling mechanisms like you try to actively cool that mode and if you would actively cool it maybe physically the wave guide could be warmer and and your protocol could could still work but in The end for example this this whole idea will will not work very well at 4 Kelvin because then at some stage the the loss in the wave guide itself will will become significant and so I I think the complexity of yeah yeah the even if it Was niobia more so like for example in this in this 2017 paper where we've looked at these different wave guide Technologies we've measured loss versus temperature and and sort of it rapidly degrades as the as the the super conductor gets worse so I I think the physics is Interesting to explore but on a practical level I think in this um maybe it would have been a little bit easier by by reducing the temperature con constraints a little bit but but not drastically so so we decided to go um to go all the way and in particular like The Bell test experiments were done with this uh um with this isolate or with the circulator in the line and that you can also used to to First measure the background temperature in the line and also to cool it to have it thermalized to some cold load you understand this right that the Weak point in this lool Fess is still this this random number generator but seems like it's a principal problem there you can't do anything if you assume that there hidden variables and you want to prove that they are not and but if there would be Vis variables you Canot have a random number generator right there could be I think this this people ref argument is it yeah this this this people refer to as as sort of super determinism and this you can't exclude with any experiment that you could do so so there's um therefore there's maybe Okay some some people I mean you could ask yourself would you talk of a loophole free belt test or so that that that gets done frequently but you could also talk about about Bel tests which uh which avoid assumpt or which which don't need assumptions about locality or or or Or Fair sampling for example and and and so we decided to still go for calling this a loophole free um um experiment because we essentially use the same criteria as the other experiments that that were done in this loophole free category but in principle this these super deterministic ideas you can't Exclude with experiments like guess you random generators based on the assumptions of quantum mechanics you then want to prove um yes but but there's like even if you don't assume like the super deterministic models that it really it doesn't matter if you if you think there's correlations built in into the Universe that that or that there's essentially no no free choice anywhere neither in humans nor nor in any of of the physics that happens around you then then you just can't say any it could all be predetermined and and you wouldn't notice and and and so I think that's Something that no experiment can can can can exclude and so um so also the reason so we started this experiment because there were no loophole free Bell tests when when we thought about it and started going for it and uh and and and now I think we I don't think that we've Learned anything new about the theory of it or about the interpretation by doing this particular experiment I think it it kind of addresses the the questions that are relevant in these other experiments in a similar way but in a in a physical system that is very different and where All the mechanisms that use are very different or like all the other experiments involved Optical frequency photons in some form they all work with microscopic degrees of freedom this is sort of microscopic degrees of freedom and and and the connection to using these Technologies in the qu Computing Context or so that was what what motivated us it it was not so much to to see whether this would sort of contribute to uh to to settle any of these other maybe still open questions about about the interpretation ofest type experiments and and I don't think that the our Experiment in itself has has sort of very much new to at beyond the discussions that we already have had in these contexts we have another maybe last question somewhere yeah I just was curious whether there aren people around inventing new loopholes yeah certainly I I guess this Would be a very interesting feat for people thinking about mechis I didn't follow the field are there new loop around in proposed in literature or so um I mean there there there's this one that we've just discussed that and in principle that's unavoidable and and I do think that with These with kind of these quote unquote nominally loophole free experiments I think this discussion has sort of calmed down a little bit but but there's obviously we get one or the other email after publishing this yeah and it's it's it's it's still there but but as I said I um I I don't Think that our experiment can can currently help to settle any of these questions in a in a particular way and and uh it could maybe be interesting to to to think about that and uh and I I do think that the types of discussions that We had around it um um also in the refereeing process or there there were to a large degree also discuss sort of interpretational aspects and how to talk about the observations and and terms of local causality or local realism and and and how you how you discuss these particular aspects of of Of quantum physics but our our experiments could could not add anything to that I don't think that they provide a different perspective on on those types of questions Beyond reinforcing the fact that in a very different physical system would observe similar things and and and would we have expected this Bell inequality violation Experiment to come out the way it did yes we had expected that and and probably no one else had expected anything anything different but but it's probably still worthwhile to to do the experiment to to check and then see how you could use it maybe for for potential applications later I've Mentioned some of those so if there are more question I would suggest to talk over these with coffee and cake which should be waiting in the cafeteria of us for us and so