Non-Locality Swapping and emergence of quantum correlations Nicolas Brunner Paul Skrzypczyk, Sandu Popescu University of Bristol

Entanglement versus non-locality ENTANGLEMENT (QM) NON-LOCALITY Post-quantum theories ??? Why is quantum non-locality limited ? No-signalling

Outline Post-quantum theories Genuine boxes & Non-locality swapping Connection to quantum boundary

Non-locality / CHSH game Correlation (same) Anti-correlation (opposite) Classical systems Best score = 2 Bell inequality Quantum Mechanics Best score = 2√2 Tsirelson’s bound Non-signalling Best score = 4 < ??? Score: +1 if correct -1 if wrong PR box

Popescu-Rohrlich (PR) box, NL box Non-signalling Maximally Non-local CHSH = 4 Popescu & Rohrlich, Found. Phys. 1994Barrett et al. PRA 2005 Why does the PR-box not exist in Nature ?

Black-box x,y,a,b in {0,1} Joint probability distribution P(a,b|x,y) Constraints 1.Positivity 2.No-signalling Polytope of correlations

Geometry Local Non-local PR NS polytope 8-dimensional, 24 vertices 1. Deterministic (local) boxes 2. PR (non-local) boxes PLPL PLPL PR 2

Geometry Local Non-local PR PLPL PLPL PR 2 PR PLPL PLPL Q boundary (Tsirelson,Landau, Masanes) Id

Separation PR Communication complexity PR (van Dam, 2005) Becomes trivial in specific Post-quantum theories PLPL PLPL Id Noisy PR boxes (Brassard et al., 2006) Correlated NL boxes (Brunner, Skrzypczyk, 2009)

Dynamics? Entanglement swapping Does a similar protocol exist for PR boxes ? Can joint measurements be implemented ? QM allows for rich dynamics. What about Post-quantum models ??

Non-locality swapping A theory limited only by non-signalling has poor dynamics Short Popescu Gisin (2006); Barrett (2006) Trade-off between states and dynamics PR

Genuine boxes Intuition: Some boxes are more fundamental than others

Quantum black boxes  Many boxes P(ab|xy) Classical transformations (bit flips) xy ab

Joint measurements on quantum black boxes Now it matters what Q state is in the box Open the boxes, remove circuitry !!! Genuine part of the box = real NL resource Bob AliceCharlie

Genuine PR box Difficulty for boxes: How to separate what is genuine from what is not? ONE PR box + classical transformations Freedom in choosing the set of genuine boxes = DOES matter for dynamics All 8 PR boxes (symetries) 1. All PR boxes genuine2. Single genuine PR box

Choice of genuine boxes 1. All PR boxes genuine2. Single genuine PR box  Poor dynamics  No joint measurement  Rich dynamics  Joint measurements Short et al. Barrett (2006)Here… Interesting dynamics is possible for PR boxes

Non-locality swapping New device in the theory: coupler (analogue of Q joint meas.) SUCCESS FAILURE PR

Emergence of quantum boundary Skrzypczyk, Brunner, Popescu, PRL 102, (2009) Is NL swapping still possible with noisy PR boxes? Swapping is possible iff the box is post-quantum !

Thank you!

Emergence of quantum boundary Is NL swapping still possible with noisy PR boxes? When can the noisy box used for swapping? Swapping is possible iff the box is post-quantum ! Noisy PR boxes When

Emergence of quantum boundary Boundary of swapping Tsirelson-Landau-Masanes criteria for quantumness of correlations = 2D slice of the polytope Skrzypczyk, Brunner, Popescu, PRL 102, (2009) When can noisy boxes be swapped? iff the boxes are post-quantum

Consistency 2. Coupler can be applied directly to any allowed box 1. Bob cannot signal by applying the coupler All 8 PR boxes genuine Single genuine PR box works ! PR

Connection to Bell inequalities Coupler ≈ CHSH Coupler reveals a joint property of the box Coupler Bell Inequality Skrzypczyk, Brunner, arxiv:

Supp. 1: Bell’s inequality  Quantum Correlations: Clauser-Horne-Shimony-Holt (CHSH), PRL 1969 QM violates Bell’s inequality Bell’s inequality (CHSH) Bell’s inequality holds for ANY local theory

Supp. 2: Post-quantum model 1.Non-signalling 2. Maximally Non-local (more NL than QM 2√2) CHSH  4 CHSH = C 00 + C 01 + C 10 – C 11 Popescu & Rohrlich, Found. Phys Barrett et al. PRA 2005 Non-local box of Popescu and Rohrlich (PR-box) Why does the PR-box not exist in Nature ?