Survey on Nonlocal Games and Operator Space Theory

Abstract

This review article is concerned with a recently uncovered connection between operator spaces, a noncommutative extension of Banach spaces, and quantum nonlocality, a striking phenomenon which underlies many of the applications of quantum mechanics to information theory, cryptography and algorithms. Using the framework of nonlocal games, we relate measures of the nonlocality of quantum mechanics to certain norms in the Banach and operator space categories. We survey recent results that exploit this connection to derive large violations of Bell inequalities, study the complexity of the classical and quantum values of games and their relation to Grothendieck inequalities, and quantify the nonlocality of different classes of entangled states.

48 pages, comments welcome

References in corpus (7)

• Experimental loophole-free violation of a Bell inequality using entangled electron spins separated by 1.3 km
• Connes' embedding problem and Tsirelson's problem
• Unbounded violation of tripartite Bell inequalities
• Parallel repetition and concentration for (sub-)no-signalling games via a flexible constrained de Finetti reduction
• Large bipartite Bell violations with dichotomic measurements
• Tripartite Bell inequality, random matrices and trilinear forms
• The Hilbertian Tensor Norm and Entangled Two-Prover Games

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• Bell nonlocality with a single shot
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• Quantum Query Algorithms are Completely Bounded Forms
• Bell's nonlocality in a general nonsignaling case: quantitatively and conceptually
• Regarding the Maximal Qubit Violations of n-Locality in Star and Chain Networks
• On the separation of correlation-assisted sum capacities of multiple access channels
• Device independent security of quantum key distribution from monogamy-of-entanglement games
• Synergies Between Operations Research and Quantum Information Science
• Reducing the number of inputs in nonlocal games
• Entangled Rendezvous: A Possible Application of Bell Non-Locality For Mobile Agents on Networks
• On the existence of a local quasi hidden variable (LqHV) model for each N-qudit state and the maximal quantum violation of Bell inequalities
• Correlations constrained by composite measurements
• Undecidability in Physics: a Review
• Random constructions in Bell inequalities: A survey
• Teleportation with Embezzling Catalysts
• New concise upper bounds on quantum violation of general multipartite Bell inequalities
• The Ramsey property for Operator spaces and noncommutative Choquet simplices
• Measurement incompatibility vs. Bell non-locality: an approach via tensor norms
• Heralded Channel Holevo Superadditivity Bounds from Entanglement Monogamy
• Communication with Quantum Catalysts
• Specifying nonlocality of a pure bipartite state and analytical relations between measures for bipartite nonlocality and entanglement
• Classical bounds on two-outcome bipartite Bell expressions and linear prepare-and-measure witnesses: Efficient computation in parallel environments such as graphics processing units
• Unbounded Bell violations for quantum genuine multipartite non-locality
• Orthogonality Broadcasting and Quantum Position Verification
• Failure of the trilinear operator space Grothendieck theorem
• On random classical marginal problems with applications to quantum information theory