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NearOptimal and Explicit Bell Inequality Violations
"... Bell inequality violations correspond to behavior of entangled quantum systems that cannot be simulated classically. We give two new twoplayer games with Bell inequality violations that are stronger, fully explicit, and arguably simpler than earlier work. The first game is based on the Hidden Match ..."
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Bell inequality violations correspond to behavior of entangled quantum systems that cannot be simulated classically. We give two new twoplayer games with Bell inequality violations that are stronger, fully explicit, and arguably simpler than earlier work. The first game is based on the Hidden Matching problem of quantum communication complexity, introduced by BarYossef, Jayram, and Kerenidis. This game can be won with probability 1 by a quantum strategy using a maximally entangled state with local dimension n (e.g., log n EPRpairs), while we show that the winning probability of any classical strategy differs from 1 2 by at most O(log n/ √ n). The second game is based on the integrality gap for Unique Games by Khot and Vishnoi and the quantum rounding procedure of Kempe, Regev, and Toner. Here ndimensional entanglement allows to win the game with probability 1/(logn) 2, while the best winning probability without entanglement is 1/n. This nearlinear ratio (“Bell inequality violation”) is nearoptimal, both in terms of the local dimension of the entangled state, and in terms of the number of possible outputs of the two players.
On the largest Bell violation attainable by a quantum state. ArXiv 1206.3695
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THEORY OF COMPUTING www.theoryofcomputing.org NearOptimal and Explicit Bell Inequality Violations ∗
, 2012
"... Abstract: Entangled quantum systems can exhibit correlations that cannot be simulated classically. For historical reasons such correlations are called “Bell inequality violations.” We give two new twoplayer games with Bell inequality violations that are stronger, fully explicit, and arguably simple ..."
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Abstract: Entangled quantum systems can exhibit correlations that cannot be simulated classically. For historical reasons such correlations are called “Bell inequality violations.” We give two new twoplayer games with Bell inequality violations that are stronger, fully explicit, and arguably simpler than earlier work. The first game is based on the Hidden Matching problem of quantum communication complexity, introduced by BarYossef, Jayram, and Kerenidis. This game can be won with probability 1 by a strategy using a maximally entangled state with local dimension n (e. g., logn EPRpairs), while we show that the winning probability of any classical strategy differs from 1 2 by at most O(log(n)/√n). The second game is based on the integrality gap for Unique Games by Khot and Vishnoi and the quantum rounding procedure of Kempe, Regev, and Toner. Here ndimensional
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"... Abstract: Entangled quantum systems can exhibit correlations that cannot be simulated classically. For historical reasons such correlations are called “Bell inequality violations.” We give two new twoplayer games with Bell inequality violations that are stronger, fully explicit, and arguably simple ..."
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Abstract: Entangled quantum systems can exhibit correlations that cannot be simulated classically. For historical reasons such correlations are called “Bell inequality violations.” We give two new twoplayer games with Bell inequality violations that are stronger, fully explicit, and arguably simpler than earlier work. The first game is based on the Hidden Matching problem of quantum communication complexity, introduced by BarYossef, Jayram, and Kerenidis. This game can be won with probability 1 by a strategy using a maximally entangled state with local dimension n (e. g., logn EPRpairs), while we show that the winning probability of any classical strategy differs from 1/2 by at most O((logn) / √ n).
QUANTUMPROOF RANDOMNESS EXTRACTORS VIA OPERATOR SPACE THEORY
"... Abstract. Randomness extractors are an important building block for classical and quantum cryptography as well as for device independent randomness amplification and expansion. It is known that some constructions are quantumproof whereas others are provably not [Gavinsky et al., STOC’07]. We argue ..."
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Abstract. Randomness extractors are an important building block for classical and quantum cryptography as well as for device independent randomness amplification and expansion. It is known that some constructions are quantumproof whereas others are provably not [Gavinsky et al., STOC’07]. We argue that the theory of operator spaces offers a natural framework for studying to what extent objects are quantumproof: we first rephrase the definition of extractors as a bounded norm condition between normed spaces, and then show that the presence of quantum adversaries corresponds to a completely bounded norm condition between operator spaces. Using semidefinite programming (SDP) relaxations of this completely bounded norm, we recover all known classes of quantumproof extractors as well as derive new ones. Furthermore, we provide a characterization of randomness condensers (which correspond to a generalization of extractors) and their quantumproof properties in terms of twoplayer games. Full Technical Version: arXiv:1409.3563. Introduction. In cryptographic protocols such as key distribution and randomness expansion, it is often possible to guarantee that an adversary’s knowledge about the secret N held by honest players is bounded. The relevant quantity in many settings is the adversary’s guessing probability of the
CBNORM ESTIMATES FOR MAPS BETWEEN NONCOMMUTATIVE LpSPACES AND QUANTUM CHANNEL THEORY
"... Abstract. In the first part of this work we show how certain techniques from quantum information theory can be used in order to obtain very sharp embeddings between noncommutative Lpspaces. Then, we use these estimates to study the classical capacity with restricted assisted entanglement of the qu ..."
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Abstract. In the first part of this work we show how certain techniques from quantum information theory can be used in order to obtain very sharp embeddings between noncommutative Lpspaces. Then, we use these estimates to study the classical capacity with restricted assisted entanglement of the quantum erasure channel and the quantum depolarizing channel. In particular, we exactly compute the capacity of the first one and we show that certain nonmultiplicative results hold for the second one. 1.