Nonviolation of Bell's inequality in translation invariant systems

Instituto de Física, Universidade Federal Fluminense - Av. Gal. Milton Tavares de Souza s/n, Gragoatá 24210-346, Niterói, RJ, Brazil

^(a) tro@if.uff.br

Received: 31 October 2012
Accepted: 27 November 2012

Abstract

The nature of quantum correlations in strongly correlated systems has been a subject of intense research. In particular, it has been realized that entanglement and quantum discord are present at quantum phase transitions and are able to characterize them. Surprisingly, it has been shown for a number of different systems that qubit pairwise states, even when highly entangled, do not violate Bell's inequalities, being in this sense local. Here we show that such a local character of quantum correlations traces back to the the monogamy trade-off obeyed by bipartite Bell correlations, being in fact general for translation invariant systems. We illustrate this result in a quantum spin chain with a soft breaking of translation symmetry. In addition, we provide an extension of the monogamy inequality to the N-qubit scenario, showing that the bound increases with N and providing examples of its saturation through uniformly generated random pure states.