Bell Non-Locality in Many Body Quantum Systems with Exponential Decay of Correlations

Abstract

Using Bell-inequalities as a tool to explore non-classical physical behaviours, in this paper we analyse what one can expect to find in many-body quantum physics. Concretely, framing the usual correlation scenarios as a concrete spin-lattice, we want know whether or not it is possible to violate a Bell-inequality restricted to this scenario. Using clustering theorems, we are able to show that a large family of quantum many-body systems behave almost locally, violating Bell-inequalities (if so) only by a non-significant amount. We also provide examples, explain some of our assumptions via counter-examples and present all the proofs for our theorems. We hope the paper is self-contained.

General spin systems without genuinely multipartite nonlocality

“…It means that the quantum correlations for the gapped ground states will not significantly violate any npartite Bell inequality ( 7) when all the involved regions are far away from each other. This is different from recent result by clustering N -particle systems to N uncorrelated parties [55].…”

“…This means that these thermal states show almost no obvious genuinely multipartite nonlocality by using two kinds of exponentially clustering correlations. These are going beyond recent results with different clustering theorems [55].…”

“…of genuine tripartite entanglement [52]. Moreover, if the observable is acted on distant regions of the lattice, the ground state of gapped Hamiltonian behave almost locally by clustering the bipartite system into two uncorrelated particles [55]. Combing with Lemma 1, we show that the ground state of gapped Hamiltonian is unable to significantly violate any Bell inequality (6) when the involved regions are far apart, that is, there is almost no genuinely tripartite nonlocality for the ground state.…”

“…It is also useful for ground and thermal states defined on any lattice geometry [54]. Especially, by clustering the systems into two independent parts in term of CHSH scenario [27], the nonlocality cannot be observed in the experiment for two regions being far enough [55]. Here, we prove a thermal state ρ being acted on the lattice at any inverse temperature β < β * is ǫ-local [68].…”

“…Our motivation in this work is to find necessary condition for spin systems in lattice. The main idea is inspired by the exponentially clustering correlations [55]. We show that any local measurements acting on remote regions of given quantum spin systems cannot create genuinely multipartite nonlocal correlations in terms of any Svetlichny-type inequality in the biseparable model [31].…”