New Localizable Entanglement

TL;DR

This paper clarifies and introduces a new form of localizable entanglement (NLE), analyzing its relationship with LE across systems of varying sizes, revealing that NLE is generally less or equal to LE and highlighting differences in larger systems.

Contribution

The paper defines and explores a new form of localizable entanglement, NLE, and compares it with LE, especially in multi-component quantum systems, addressing ambiguities in the original concept.

Findings

NLE is always less than or equal to LE.

For three-component systems, NLE and LE are similar.

Differences between NLE and LE grow with more components.

Abstract

In this study, we have addressed an ambiguity in the concept of localizable entanglement (LE) introduced by Verstraete et al in 2004. By doing so, we have proposed and explored a unique form of this entanglement, called new localizable entanglement (NLE). We have shown that NLE is always less than or equal to LE. Additionally, we have demonstrated that for systems with three components, NLE does not differ significantly from LE. However, when the number of components increases to four, there is a possibility of significant differences between the two methods. Furthermore, as the number of components increases further, this difference becomes slightly more pronounced. It appears that the classical correlation, which is the lower bound for LE, is also a lower bound for NLE.