# Operator Space theory: a natural framework for Bell inequalities

### Impacto

Junge, M. and Pérez García, David and Palazuelos Cabezón, Carlos and Villanueva, Ignacio and Wolf, Michael (2009) Operator Space theory: a natural framework for Bell inequalities. Physical Review Letters, 104 . ISSN 0031-9007, ESSN: 1079-7114

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## Abstract

In this letter we show that the field of Operator Space Theory provides a general and powerful mathematical framework for arbitrary Bell inequalities, in particular regarding the scaling of their violation within quantum mechanics. We illustrate the power of this connection by showing that bipartite quantum states with local Hilbert space dimension n can violate a Bell inequality by a factor of order $\frac{\sqrt{n}}{\log^2n}$ when observables with n possible outcomes are used. Applications to resistance to noise, Hilbert space dimension estimates and communication complexity are given.

Item Type: Article Short (non-technical) version Teoría cuántica Quantum Physics Sciences > Physics > Mathematical physicsSciences > Physics > Quantum theory 12160 03 Feb 2011 09:12 03 Dec 2014 12:45