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Palazuelos Cabezón, Carlos
(2014)
*On the largest Bell violation attainable by a quantum state.*
Journal of functional analysis, 267
(7).
pp. 1959-1985.

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Official URL: http://www.sciencedirect.com/science/article/pii/S0022123614003140

## Abstract

We study the projective tensor norm as a measure of the largest Bell violation of a quantum state. In order to do this, we consider a truncated version of a well-known SDP relaxation for the quantum value of a two-prover one-round game, one which has extra restrictions on the dimension of the SDP solutions. Our main result provides a quite accurate upper bound for the distance between the classical value of a Bell inequality and the corresponding value of the relaxation. Along the way, we give a simple proof that the best complementation constant of l(2)(n) in l(1) (l(infinity)) is of order root ln n As a direct consequence, we show that we cannot remove a logarithmic factor when we are computing the largest Bell violation attainable by the maximally entangled state.

Item Type: | Article |
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Uncontrolled Keywords: | Quantum information theory; Bell inequalities; Projective tensor norm; Hilbertian subspaces |

Subjects: | Sciences > Mathematics > Mathematical analysis |

ID Code: | 27289 |

Deposited On: | 06 Nov 2014 08:33 |

Last Modified: | 14 Jan 2015 11:31 |

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