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

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: |11>  () |00>

1. 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.

Satigny – Geneva – Jussy 18.0 km δ Geneva

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.

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

Leggett’s inequalities

Leggett’s inequalities

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

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

Experimental refutation of Leggett’s model 1.4 1.5 1.6 1.7 1.8 1.9 2 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° 30° 60° 90°  PRL 99,210406,2007 PRL 99,210407,2007 Branciard et al. Quant-ph/0801.2241 Nature Physics, in press, 2008 for 60 sec/setting: L3(-30°)=5.7204±0.0028 (83.7 σ)

5. Simulation with a PR-box Alice Bob x {0,1} y{0,1} a + b= x.y a {0,1} b {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

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

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 …

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

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 ? product state max entangl.

From asymmetric detection loophole to the impossibility of simulating with a PR-box =x(,a) =y(,b) =(,a, a) = (,b,b) x y 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 Asymmetric detection: Alice Bob if xg = x(,a) = (, b, ag +xg.y(,b)) then =(,a,ag) else “no output”

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.

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.

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

7. Correlated local flips Let’s try to make up the non-trivial marginal afterwards. Let 1 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  no flip  flip  but not  where  flip  and  quant-ph/0803.2359

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

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

8. The M-box (Millionaire-box) Alice Bob x [0,1] 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 Inn22 Bell inequalities. quant-ph/0803.2359

Simulating entangled qubits with 4 PR-boxes and 1 M-box quant-ph/0803.2359

Simulating entangled qubits with 4 PR-boxes and 1 M-box a+b=xy a+b=xy b1 a2 b2 a1 az bz a+b=(xy) a b quant-ph/0803.2359

Simulating entangled qubits with 4 PR-boxes and 1 M-box a+b=xy a+b=xy b1 a2 b2 a1 az bz a+b=(xy) a b a+b=xy b a 1 1 2 2

Simulating entangled qubits with 4 PR-boxes and 1 M-box   local flip fa local flip fb   quant-ph/0803.2359

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

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 !?!

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.

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

Let’s test these hypothetical preferred reference frame Alice and Bob, east-west orientation, perfect synchronization with respect to earth 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

D. Salard et al., Nature, 2008

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

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

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

Bell test with true space-like separation source A B time space A macroscopic mass has significantly moved  60 s  18 km  7 s 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

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