Entanglement and Nonlocality in Infinite 1D Systems

TL;DR

This paper develops methods to detect entanglement and nonlocality in infinite 1D translation-invariant systems using only near-neighbor information, revealing complex structures and violations of Bell inequalities.

Contribution

It provides a characterization of local states in infinite TI spin chains, constructs entanglement witnesses, and devises procedures to identify Bell inequality violations in such systems.

Findings

Existence of local separable states with only entangled TI extensions

Construction of linear entanglement witnesses from nearest-neighbor data

Demonstration of Bell inequality violations in infinite TI states

Abstract

We consider the problem of detecting entanglement and nonlocality in one-dimensional (1D) infinite, translation-invariant (TI) systems when just near-neighbor information is available. This issue is deeper than one might think a priori, since, as we show, there exist instances of local separable states (classical boxes) which admit only entangled (nonclassical) TI extensions. We provide a simple characterization of the set of local states of multiseparable TI spin chains and construct a family of linear witnesses which can detect entanglement in infinite TI states from the nearest-neighbor reduced density matrix. Similarly, we prove that the set of classical TI boxes forms a polytope and devise a general procedure to generate all Bell inequalities which characterize it. Using an algorithm based on matrix product states, we show how some of them can be violated by distant parties conducting identical measurements on an infinite TI quantum state. All our results can be easily adapted to detect entanglement and nonlocality in large (finite, not TI) 1D condensed matter systems.