NonLocality Swapping and emergence of quantum correlations Nicolas

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

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

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

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

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

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

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

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

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

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

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

Genuine boxes Intuition: Some boxes are more fundamental than others

Quantum black boxes x y a b • Many boxes P(ab|xy) • Classical transformations (bit flips)

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

Genuine PR box Difficulty for boxes: How to separate what is genuine from what is not? ONE PR box + classical transformations All 8 PR boxes (symetries) Freedom in choosing the set of genuine boxes 1. All PR boxes genuine 2. Single genuine PR box = DOES matter for dynamics

Choice of genuine boxes 1. All PR boxes genuine 2. Single genuine PR box Ø Poor dynamics Ø No joint measurement Ø Rich dynamics Ø Joint measurements Short et al. Barrett (2006) Here… Interesting dynamics is possible for PR boxes

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

Emergence of quantum boundary Is NL swapping still possible with noisy PR boxes? Swapping is possible iff the box is post-quantum ! Skrzypczyk, Brunner, Popescu, PRL 102, 110402 (2009)

Thank you!

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

Emergence of quantum boundary 2 D slice of the polytope When can noisy boxes be swapped? iff the boxes are post-quantum Boundary of swapping = Tsirelson-Landau-Masanes criteria for quantumness of correlations Skrzypczyk, Brunner, Popescu, PRL 102, 110402 (2009)

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

Connection to Bell inequalities Bell Inequality Coupler ≈ CHSH Coupler reveals a joint property of the box Skrzypczyk, Brunner, arxiv: 08120758

Supp. 1: Bell’s inequality + + a={+1, -1} - - b={+1, -1} Bell’s inequality (CHSH) Clauser-Horne-Shimony-Holt (CHSH), PRL 1969 Bell’s inequality holds for ANY local theory Quantum Correlations: QM violates Bell’s inequality

Supp. 2: Post-quantum model Non-local box of Popescu and Rohrlich (PR-box) Popescu & Rohrlich, Found. Phys. 1994 Barrett et al. PRA 2005 1. Non-signalling 2. Maximally Non-local (more NL than QM 2√ 2) CHSH = C 00 + C 01 + C 10 – C 11 Why does the PR-box not exist in Nature ? CHSH 4