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Consequences and Limits of Nonlocal Strategies
, 2010
"... Thispaperinvestigatesthepowersandlimitationsofquantum entanglementinthecontext of cooperative games of incomplete information. We give several examples of such nonlocal games where strategies that make use of entanglement outperform all possible classical strategies. One implication ofthese examples ..."
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Cited by 120 (20 self)
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Thispaperinvestigatesthepowersandlimitationsofquantum entanglementinthecontext of cooperative games of incomplete information. We give several examples of such nonlocal games where strategies that make use of entanglement outperform all possible classical strategies. One implication ofthese examplesis that entanglement canprofoundly affectthesoundness property of twoprover interactive proof systems. We then establish limits on the probability with which strategies making use of entanglement can win restricted types of nonlocal games. These upperbounds mayberegardedasgeneralizationsof Tsirelsontypeinequalities, which place bounds on the extent to which quantum information can allow for the violation of Bell inequalities. We also investigate the amount of entanglement required by optimal and nearly optimal quantum strategies forsome games.
Unbounded violations of bipartite Bell inequalities via Operator Space theory
 Communications in Mathematical Physics, 300(3):715–739, 2010. arXiv:0910.4228. Shorter version appeared in PRL 104:170405, arXiv:0912.1941
"... Abstract: In this work we show that bipartite quantum states with local Hilbert space dimension n can violate a Bell inequality by a factor of order Ω n log2 n when observables with n possible outcomes are used. A central tool in the analysis is a close relation between this problem and operator sp ..."
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Cited by 17 (2 self)
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Abstract: In this work we show that bipartite quantum states with local Hilbert space dimension n can violate a Bell inequality by a factor of order Ω n log2 n when observables with n possible outcomes are used. A central tool in the analysis is a close relation between this problem and operator space theory and, in particular, the very recent noncommutative Lp embedding theory. As a consequence of this result, we obtain better Hilbert space dimension witnesses and quantum violations of Bell inequalities with better resistance to noise. 1.
Tsirelson’s Problem and Kirchberg’s Conjecture
, 2010
"... This document is an extended abstract of [Fri10b]. See [JNP + 10] for closely related results obtained by different methods. Quantum correlations in composite quantum systems. In the study of quantum entanglement and quantum correlations, one usually assumes that the state space of a composite quant ..."
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Cited by 12 (2 self)
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This document is an extended abstract of [Fri10b]. See [JNP + 10] for closely related results obtained by different methods. Quantum correlations in composite quantum systems. In the study of quantum entanglement and quantum correlations, one usually assumes that the state space of a composite quantum system is a tensor product HA ⊗ HB, so that the correlations take on the form P (a, b  x, y) = 〈ψ, (A a x ⊗ B b y)ψ〉. (1) with POVM observables Ax a and B y b. However, how is this justified from physical principles? Can we really be sure that this tensor product assumption is appropriate? One possible alternative assumption might be to say that a composite system is defined in terms of a joint Hilbert space H together with, for each site, a set of local observables on H, such that each observable located on the first site commutes with each observable located on the second site; in physical terms, this means that the observables located at different sites are compatible, and can in particular be measured jointly. This is the “commutativity assumption”. In the case of finitedimensional case, this is effectively equivalent to the
Large violation of Bell inequalities with low entanglement
 Comm. Math. Phys
"... Abstract. In this paper we obtain violations of general bipartite Bell inequalities of order n logn with n inputs, n outputs and ndimensional Hilbert spaces. Moreover, we construct explicitly, up to a random choice of signs, all the elements involved in such violations: the coefficients of the Bell ..."
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Cited by 12 (3 self)
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Abstract. In this paper we obtain violations of general bipartite Bell inequalities of order n logn with n inputs, n outputs and ndimensional Hilbert spaces. Moreover, we construct explicitly, up to a random choice of signs, all the elements involved in such violations: the coefficients of the Bell inequalities, POVMs measurements and quantum states. Analyzing this construction we find that, even though entanglement is necessary to obtain violation of Bell inequalities, the Entropy of entanglement of the underlying state is essentially irrelevant in obtaining large violation. We also indicate why the maximally entangled state is a rather poor candidate in producing large violations with arbitrary coefficients. However, we also show that for Bell inequalities with positive coefficients (in particular, games) the maximally entangled state achieves the largest violation up to a logarithmic factor. 1. Introduction and
Nonlocality and Communication Complexity
, 2009
"... Quantum information processing is the emerging field that defines and realizes computing devices that make use of quantum mechanical principles, like the superposition principle, entanglement, and interference. Until recently the common notion of computing was based on classical mechanics, and did n ..."
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Quantum information processing is the emerging field that defines and realizes computing devices that make use of quantum mechanical principles, like the superposition principle, entanglement, and interference. Until recently the common notion of computing was based on classical mechanics, and did not take into account all the possibilities that physicallyrealizable computing devices offer in principle. The field gained momentum after Peter Shor developed an efficient algorithm for factoring numbers, demonstrating the potential computing powers that quantum computing devices can unleash. In this review we study the information counterpart of computing. It was realized early on by Holevo, that quantum bits, the quantum mechanical counterpart of classical bits, cannot be used for efficient transformation of information, in the sense that arbitrary kbit messages can not be compressed into messages of k − 1 qubits. The abstract form of the distributed computing setting is called communication complexity. It studies the amount of information, in terms of bits or in our case qubits, that two spatially separated computing devices need to exchange in order to perform some computational task. Surprisingly
The convex Positivstellensatz in a free algebra
"... Abstract. Given a monic linear pencil L in g variables, let P L = (P L (n)) n∈N where and S g n is the set of gtuples of symmetric n × n matrices. Because L is a monic linear pencil, each P L (n) is convex with interior, and conversely it is known that convex bounded noncommutative semialgebraic s ..."
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Abstract. Given a monic linear pencil L in g variables, let P L = (P L (n)) n∈N where and S g n is the set of gtuples of symmetric n × n matrices. Because L is a monic linear pencil, each P L (n) is convex with interior, and conversely it is known that convex bounded noncommutative semialgebraic sets with interior are all of the form P L . The main result of this paper establishes a perfect noncommutative Nichtnegativstellensatz on a convex semialgebraic set. Namely, a noncommutative matrixvalued polynomial p is positive semidefinite on P L if and only if it has a weighted sum of squares representation with optimal degree bounds: where s, f j are matrices of noncommutative polynomials of degree no greater than 2 . This noncommutative result contrasts sharply with the commutative setting, where there is no control on the degrees of s, f j and assuming only p nonnegative, as opposed to p strictly positive, yields a clean Positivstellensatz so seldom that such cases are noteworthy.
Monogamy of nonlocal quantum correlations
 Tsi06] Boris S. Tsirelson. Bell inequalities and operator algebras (Problem 33). In Quantum Information: Open Problems
, 2009
"... We describe a new technique for obtaining Tsirelson bounds, or upper bounds on the quantum value of a Bell inequality. Since quantum correlations do not allow signaling, we obtain a Tsirelson bound by maximizing over all nosignaling probability distributions. This maximization can be cast as a line ..."
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Cited by 11 (2 self)
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We describe a new technique for obtaining Tsirelson bounds, or upper bounds on the quantum value of a Bell inequality. Since quantum correlations do not allow signaling, we obtain a Tsirelson bound by maximizing over all nosignaling probability distributions. This maximization can be cast as a linear program. In a setting where three parties, A, B, and C, share an entangled quantum state of arbitrary dimension, we: (i) bound the tradeoff between AB’s and AC’s violation of the CHSH inequality, and (ii) demonstrate that forcing B and C to be classically correlated prevents A and B from violating certain Bell inequalities, relevant for interactive proof systems and cryptography.
Polynomialspace approximation of nosignaling provers
 In 37th international colloquium conference on Automata, languages and programming (ICALP
, 2010
"... ar ..."