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Understanding Quantum Correlations

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

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Understanding Quantum Correlations

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

  2. 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> Understanding Quantum Correlations

  3. 1. Bell locality 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.

  4. Satigny – Geneva – Jussy Satigny Jussy 18.0 km δ Geneva

  5. How come the correlation ? • 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.

  6. 4. Leggett’s “locality” Found.Phys. 10,1469,2003; Vienna, Nature 2006; A. Suarez, Found. Phys. 2008 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

  7. Leggett’s inequalities

  8. Leggett’s inequalities

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

  10. Experimental Setup Traditional Type-II parametric down conversion source: • photon pairs @702nm • HV: vis= 98.9±0.8% • ±45°: vis=97.8±0.8% • max. coincidence rate:630 s-1,accidentals: 0.3 s-1

  11. Experimental refutation of Leggett’s model 2 1.9 1.8 1.7 1.6 1.5 1.4 • integration time:4 x 15 sec / setting • maximal violation:L=1.925 ± 0.0017(40.6 σ) at φ = -25°L=1.922 ± 0.0017(38.1 σ) at φ = +25° QM L3 Leggett -90° -60° -30° 0 30° 60° 90°  PRL 99,210406,2007PRL 99,210407,2007Branciard et al. Quant-ph/0801.2241 Nature Physics, in press, 2008 for 60 sec/setting: L3(-30°)=5.7204±0.0028 (83.7 σ)

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

  13. 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

  14. 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 …

  15. 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

  16. Detection loophole in asymmetric entanglement with I3322 N. Brunner et al. PRL 98,2202407,2007 1/2 2/3 Minimal detection efficiency < 0.5 !! Connection to simulability with 1 bit of communication ? max entangl. product state

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

  18. 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.

  19. 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.

  20. Leggett’s “locality” revisited 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; Renner et al, PRL 2008

  21. 7. Correlated local flips • Let’s try to make up the non-trivial marginal afterwards. Let 0 1 0 1 f and let the outcomes , pass through a Z channel: 1-f Let the flip probabilities f and f be determined by a common variable [0,1]: 1 f f 0  no flip  flip  but not  where  flip  and  quant-ph/0803.2359

  22. Local flips for quantum correlations ! Let and look for the corresponding unbiased correlation:  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

  23. 7. Correlated local flips Lemma If 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

  24. 8. The M-box (Millionaire-box) Alice Bob y[0,1] x [0,1] a + b= (xy) b {0,1} a {0,1} • M-box are non-signaling. • a M-box allows one to simulate a PR-box. • a M-box violates maximally all the Inn22 Bell inequalities. quant-ph/0803.2359

  25. Simulating entangled qubits with4 PR-boxes and 1 M-box quant-ph/0803.2359

  26. Simulating entangled qubits with4 PR-boxes and 1 M-box a+b=xy a+b=xy a+b=(xy) az bz a b b1 b2 a2 a1 quant-ph/0803.2359

  27. Simulating entangled qubits with4 PR-boxes and 1 M-box a+b=xy a+b=xy a+b=(xy) a+b=xy a+b=xy az bz a b b a 1 1 2 2 b1 b2 a2 a1

  28. Simulating entangled qubits with4 PR-boxes and 1 M-box   local flip fa local flip fb   quant-ph/0803.2359

  29. 9. decomposition into local+nonlocal lemma: ifPL(,|a,b) = PL(,|az,bz) then pl 1-sin() V. Scarani, Quant-ph/0712.2307 PRA 2008 proof: EPR2 Phys. Lett. A 162, 25, 1992 PQM = pl.PL + (1-pl).PNL

  30. 9. decomposition into local+nonlocal 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 !?!

  31. Simulating PNL with nonlocal non-signaling resources • PNL can be simulated with 4 PR-boxes and one M-box, 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.

  32. 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

  33. Let’s test these hypothetical preferred reference frame • 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 hypothe- tical privileged frames are scanned. A B Ph. Eberhard, private communication

  34. D. Salard et al., Nature, 2008

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

  36. = 60 s Satigny Jussy 18.0 km Piezo Piezo APD FM APD FM classical channels δ FM FM 17.5 km 17.5 km quantum channel quantum channel 10.7 km 8.2 km TAC FG FBG C C Geneva FBG L F PPLN Laser 1573.5 nm 1568.5 nm A. Kent arXiv:gr-qc/0507045 Franson interferometer quant-ph/0803.2425 PRL 2008

  37. He-Ne Laser Mirror - Piezo BS Mirror + 100 nm 4V Single-photon detector Photodiode quant-ph/0803.2425

  38. Bell test with true space-like separation time  7 s A B space source A macroscopic mass has significantly moved  60 s  18 km The photon enters the interferometer 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

  39. Visibility > 90%  nonlocal correlations between truly space-like separated events. quant-ph/0803.2425; PRL 2008

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