Understanding Quantum Correlations Nicolas Gisin Cyril Branciard Nicolas

Understanding Quantum Correlations Nicolas Gisin Cyril Branciard, Nicolas Brunner GAP Optique Geneva University Group of Applied Physics Geneva university Switzerland x Alice Bob y a + b= x. y -1 0 0 -2 +1 +1 +1 -1 0 0 a b 1

GAP Optique Geneva University Understanding Quantum Correlations • Intuition • decomposition into "simpler" correlations • simulation with "simpler“ correlations • resources provided by Q correlations • resources needed to simulate Q correlations ( )=cos( /2) |00> + sin( /2) |11> where , = ± 1 no-signaling: |00> |11> ( ) 2

1. Bell locality GAP Optique Geneva University Bell locality By far the most natural assumption ! … refuted beyond (almost) any reasonable doubts. Hence, quantum correlations happen, but the probabilities of their occurrence are not determined by local variables. 3

Satigny – Geneva – Jussy Satigny 18. 0 km Jussy δ Geneva 4

How come the correlation ? GAP Optique Geneva University § How can these two locations out there in space-time know about each other ? There is no spooky action at a distance : there is not a first event that influences a second event. Quantum correlation just happen, somehow from outside space-time : there is no story in space-time that can tell us how it happens. 5

4. Leggett’s “locality” Found. Phys. 10, 1469, 2003; Vienna, Nature 2006; A. Suarez, Found. Phys. 2008 GAP Optique Geneva University Assume that locally everything is “normal”, i. e. that individual particles are always in pure states: where and “Only” the correlations C are nonlocal. They just happen, without any classical explanation. They are only constraint by P 0 6

GAP Optique Geneva University Leggett’s inequalities 7

GAP Optique Geneva University Leggett’s inequalities 8

GAP Optique Geneva University Leggett’s inequalities Modern form of Leggett’s inequality In strong contrast to Bell’s inequalities, here the bound depends on the measurement settings 9

Experimental Setup GAP Optique Geneva University Traditional Type-II parametric down conversion source: photon pairs @702 nm HV: vis= 98. 9± 0. 8% ± 45°: vis=97. 8± 0. 8% max. coincidence rate: 630 s-1, accidentals: 0. 3 s-1

Experimental refutation of Leggett’s model 2 1. 9 integration time: 4 x 15 sec / setting maximal violation: L=1. 925 ± 0. 0017 (40. 6 σ) at φ = -25° QM GAP Optique Geneva University 1. 8 L 3 Leggett 1. 7 1. 6 L=1. 922 ± 0. 0017 (38. 1 σ) at φ = +25° 1. 5 1. 4 -90° -60° -30° 0 30° for 60 sec/setting: L 3(-30°)=5. 7204± 0. 0028 (83. 7 σ) 60° 90° PRL 99, 210406, 2007 PRL 99, 210407, 2007 Branciard et al. Quant-ph/0801. 2241 Nature Physics, in press, 2008

5. Simulation with a PR-box x {0, 1} Alice Bob y {0, 1} GAP Optique Geneva University a + b= x. y a {0, 1} a + b= x. y b {0, 1} A single bit of communication suffice to simulate Prob(a=1|x, y) = ½, independent of y no signaling the PR-box (assuming shared randomness). But the PR-box does not allow any communication. E(a, b|0, 0) + E(a, b|0, 1) + E(a, b|1, 0) - E(a, b|1, 1) = 4 Hence, the PR-box is a strictly weaker resource than communication. Found. Phys. 24, 379, 1994 12

GAP Optique Geneva University Simulating a singlet with a PR-box where the are uniformly distributed on the sphere and is defined by the PR-box as follows: a + b= x. y PRL 94, 220403, 2005 Quant-ph/0507120 13

GAP Optique Geneva University Does this help our understanding ? § After all, in a PR-box the correlation merely happen, without any explanation. § Yes, but this has to be the case! § Yes, but this is also the case in quantum physics (and in models à la Leggett)! § Moreover, a+b=x. y is really simply ! § At least it helps me … 14

GAP Optique Geneva University 6. Asymmetric detection loophole § Consider entanglement between an atom and a photon. In such a case the detection of the atom can be realised with quasi 100% efficiency. § Intuition predicts and computations confirm that the threshold photon-detection efficiency is lower in such an asymmetric situation compared to the symmetric case: CHSH: max entanglement partial entanglemt A. Cabello and J. -A. Larsson, PRL 98, 220402, 2007 N. Brunner et al. , PRL 98, 220407, 2007 15

Detection loophole in asymmetric N. Brunner et al. entanglement with I 3322 PRL 98, 2202407, 2007 1/ 2 GAP Optique Geneva University 2/3 Minimal detection efficiency < 0. 5 !! Connection to simulability with 1 bit of communication ? product state max entangl. 16

From asymmetric detection loophole to the impossibility of simulating with a PR-box GAP Optique Geneva University Assume some correlation can be simulated with a PR-box: x =x( , a) y =y( , b) a+b=xy a = ( , a, a) b = ( , b, b) Let xg and ag be 2 additional shared random bits Asymmetric detection: Alice Bob if xg = x( , a) = ( , b, ag +xg. y( , b)) then = ( , a, ag) else “no output” 17

GAP Optique Geneva University Impossibility of simulating very partially entangled states with a PR-box § The fact that it is possible to close the asymmetric detection loophole with a detector’s efficiency less than 50% and partially entangled states, implies the impossibility to simulate those states with a single PR-box. 18

GAP Optique Geneva University Note on the role of marginals § We assumed a PR-box with trivial marginals and concluded that such a nonlocal resource can’t simulate quantum correlations with large marginals. § In Leggett’s model we imposed non-trivial marginals and concluded that this is incompatible with the quantum correlation corresponding to the singlets. § it is especially hard to simulate simultaneously nonlocal correlation and non-trivial marginals. 19

Leggett’s “locality” revisited GAP Optique Geneva University Assume that locally everything is “normal”, i. e. that each particle is always in a non maximally mixed state: where and where 0 1. … similar inequalities prove incompatibility with singlets Branciard et al. Quant-ph/0801. 2241 Nature Physics, 2008; 20 Renner et al, PRL 2008

7. Correlated local flips § Let’s try to make up the non-trivial marginal afterwards. Let GAP Optique Geneva University 0 and let the outcomes , pass through a Z channel: 0 f 1 1 -f 1 Let the flip probabilities f and f be determined by a common variable [0, 1]: 1 no flip f flip but not where f flip and 0 quant-ph/0803. 2359 21

Local flips for quantum correlations Let and look for the corresponding unbiased correlation: GAP Optique Geneva University and where ! is the original input moved back one step one the Hardy ladder : Hence, we almost succeeded in simulating any 2 qubit state with a PR-box … but we had to assume f f , i. e. bz az ! quant-ph/0803. 2359 22

7. Correlated local flips Lemma If GAP Optique Geneva University then there is and local flip probabilities f and f such that In words: all marginals can be realised via correlated local flips. quant-ph/0803. 2359 23

8. The M-box (Millionaire-box) GAP Optique Geneva University x [0, 1] Alice Bob y [0, 1] a + b= (x y) a {0, 1} b {0, 1} • M-box are non-signaling. • a M-box allows one to simulate a PR-box. • a M-box violates maximally all the Inn 22 Bell inequalities. quant-ph/0803. 2359 24

GAP Optique Geneva University Simulating entangled qubits with 4 PR-boxes and 1 M-box quant-ph/0803. 2359 25

Simulating entangled qubits with 4 PR-boxes and 1 M-box GAP Optique Geneva University a+b=xy a 1 a+b=xy az b 1 b 2 a 2 bz a+b=(x y) a b quant-ph/0803. 2359 26

Simulating entangled qubits with 4 PR-boxes and 1 M-box GAP Optique Geneva University a+b=xy a 1 a+b=xy az b 1 b 2 a 2 bz a+b=(x y) a b b a a+b=xy 1 2 2 27

Simulating entangled qubits with 4 PR-boxes and 1 M-box GAP Optique Geneva University local flip fa local flip fb quant-ph/0803. 2359 28

9. decomposition into local+nonlocal GAP Optique Geneva University PQM = pl. PL + (1 -pl). PNL EPR 2 Phys. Lett. A 162, 25, 1992 lemma: if PL( , |a, b) = PL( , |az, bz) then pl 1 -sin( ) V. Scarani, Quant-ph/0712. 2307 PRA 2008 proof: 29

9. decomposition into local+nonlocal GAP Optique Geneva University PQM = pl. PL + (1 -pl). PNL pl = 1 -sin( ) V. Scarani, Quant-ph/0712. 2307 PRA 2008 In the slice around the equator the nonlocal part reduces to a scalar product: but … this slice tends to zero for the singlet !? ! 30

GAP Optique Geneva University Simulating PNL with nonlocal non-signaling resources § PNL can be simulated with 4 PR-boxes and one Mbox, in a way very similar the presented one. § Consequently, partially entangled states can be simulated using nonlocal resources only in a fraction sin( ) of all cases: the less ( ) is entangled, the less frequently one needs nonlocal resources. § However, the nonlocal resources (seldomly) needed to simulate partially entangled states are definitively larger than those (always) required to simulate maximally entangled states. 31

GAP Optique Geneva University Conclusions § Q nonlocality is a mature topic. Lots of progress have been achieved, but many important and fascinating questions are still open. § Quantum correlations are very peculiar. They combine nonlocal correlations with non-trivial marginals in a way that is difficult to reproduce. § Bell-type inequalities can be derived for all kinds of hypothesis, not only Bell locality, and all sorts of nonlocal resources. § In counting resources required to simulate ( ) one should distinguish the amount of resources and the frequency at which one has to use them. § There are connections to experiments: - moving masses to ensure space-like separation - east-west Bell tests with good synchronization - asymmetric atom-photon entanglement 32

GAP Optique Geneva University Let’s test these hypothetical preferred reference frame A B Alice and Bob, east-west orientation, perfect synchronization with respect to earth perfect synchronization w. r. t any frame moving perpendicular to the A-B axis in 12 hours all hypothetical privileged frames are scanned. Ph. Eberhard, private communication 33

GAP Optique Geneva University D. Salard et al. , Nature, 2008 34

Bound on VQI/c GAP Optique Geneva University c (°) D. Salard et al. , Nature, 2008 Bound assuming the Earth’s speed is 300 km/s Bound assuming = 90 o 35

= 60 s Satigny Jussy 18. 0 km Piezo APD classical channels m. 5 k an FG FBG F PPLN Laser km. 7 10 17 mquan tum m . 5 n 1568 C TAC 1573 . 5 n el GAP Optique Geneva University a km Franson interferometer FM l km ann. 5 ch 17 tum n qu 8. 2 Geneva δ ne FM FM ch FM Piezo C L A. Kent ar. Xiv: gr-qc/0507045 quant-ph/0803. 2425 PRL 2008 36

He-Ne Laser - Mirror Piezo BS GAP Optique Geneva University Mirror + 100 nm Single-photon detector 4 V Photodiode 37 quant-ph/0803. 2425

Bell test with true space-like separation GAP Optique Geneva University time A A macroscopic mass has significantly moved The photon enters the interferometer source 60 s 18 km B 7 s space In usual Bell tests, detection events only trigger the motion of electrons of insufficient mass to finish the measurement process. quant-ph/0803. 2425 PRL 2008 38

Visibility > 90% nonlocal correlations between truly space-like separated events. GAP Optique Geneva University quant-ph/0803. 2425; PRL 2008 39