Increasing Entanglement by Separable Operations and New Monotones for W-type Entanglement

TL;DR

This paper investigates the capabilities of separable operations versus LOCC in distilling W-type entanglement, revealing a significant gap and introducing new entanglement monotones that can increase under separable operations.

Contribution

It introduces new analytic entanglement monotones for W-class states and quantifies the gap between LOCC and separable operations in entanglement distillation.

Findings

Separable operations can outperform LOCC in increasing W-state entanglement.

A gap of up to 37% exists in success probabilities between the two classes.

LOCC operations are not closed within the set of quantum measurements.

Abstract

The class of local operations and classical communication (LOCC) pertains to an important measurement scenario in many quantum communication schemes. While LOCC belongs to the more general class of separable operations (SEP), the exact difference between the two remains a challenging open problem. In this article, we seek to better understand the structure of LOCC and its relationship to SEP by comparing their respective abilities for distilling EPR entanglement from one copy of an $N$-qubit W-class state (i.e. that of the form $\sqrt{x_0}\ket{00...0}+\sqrt{x_1}\ket{10...0}+...+\sqrt{x_n}\ket{00...1}$). In terms of transformation success probability, we are able to quantify a gap as large as 37% between the two classes. Our work involves constructing new analytic entanglement monotones for W-class states which can increase on average by separable operations. Additionally, we are able to show that the set of LOCC operations, considered as a subset of the most general quantum measurements, is not closed.