Structured Negativity: A physically realizable measure of entanglement based on structural physical approximation

TL;DR

This paper introduces a new physically realizable entanglement measure called structured negativity, which satisfies entanglement properties, relates to negativity, and outperforms it in some cases, with potential laboratory implementation.

Contribution

The paper defines structured negativity as a valid entanglement measure, establishes its properties, and demonstrates its advantages over negativity and concurrence bounds.

Findings

Structured negativity satisfies entanglement monotone properties.

It relates to negativity through an established inequality.

In some cases, it provides better results than negativity and concurrence bounds.

Abstract

Quantification of entanglement is one of the most important problem in quantum information theory. In this work, we will study this problem by defining a physically realizable measure of entanglement for any arbitrary dimensional bipartite system $\rho$, which we named as structured negativity $(N_S(\rho))$. We have shown that the introduced measure satisfies the properties of a valid entanglement monotone. We also have established an inequality that relate negativity and the structured negativity. For $d\otimes d$ dimensional state, we conjecture from the result obtained in this work that negativity coincide with the structured negativity when the number of negative eigenvalues of the partially transposed matrix is equal to $\frac{d(d-1)}{2}$. Moreover, we proved that the structured negativity not only implementable in the laboratory but also a better measure of entanglement in comparison to negativity. In few cases, we obtain that structure negativity gives better result than the lower bound of the concurrence obtained by Albeverio [Phys. Rev. Lett. \textbf{95}, 040504 (2005)].