Analytic Relations between Localizable Entanglement and String Correlations in Spin Systems

TL;DR

This paper analytically explores the relationship between localizable entanglement and string correlations in quantum spin systems, revealing that localizable entanglement often simplifies to known correlation measures and can serve as perfect quantum channels.

Contribution

It provides an analytic framework linking localizable entanglement to string correlations and demonstrates conditions under which spin systems act as perfect quantum channels.

Findings

Localizable entanglement equals the average of a generalized string.

In most spin systems, localizable entanglement reduces to spin-spin or string correlations.

Certain spin 1 systems, including the Heisenberg model, can be used as perfect quantum channels.

Abstract

We study the relation between the recently defined localizable entanglement and generalized correlations in quantum spin systems. Differently from the current belief, the localizable entanglement is always given by the average of a generalized string. Using symmetry arguments we show that in most spin 1/2 and spin 1 systems the localizable entanglement reduces to the spin-spin or string correlations, respectively. We prove that a general class of spin 1 systems, which includes the Heisenberg model, can be used as perfect quantum channel. These conclusions are obtained in analytic form and confirm some results found previously on numerical grounds.