Quantifying entanglement in terms of an operational way

TL;DR

This paper introduces a new operational approach to quantify entanglement, establishing entanglement monotones linked to state conversion via LOCC, and showing their equivalence to convex roof measures in certain cases.

Contribution

It proposes a novel method to define entanglement monotones based on operational state conversion, providing a maximal measure and connecting to convex roof construction.

Findings

Entanglement monotones can be derived from pure state quantifiers.

The proposed monotone is maximal among similar measures.

In some cases, the measure is equivalent to convex roof construction.

Abstract

Quantifying entanglement is one of the most important tasks in the entanglement theory. In this paper, we establish entanglement monotones in terms of an operational approach, which is closely connected with the state conversion from pure states to the objective state by the local operations and classical communications (LOCC). It is shown that any good entanglement quantifier defined on pure states can induce an entanglement monotone for all density matrices. We especially show that our entanglement monotone is the maximal one among all that have the same form for pure states. In some particular cases, our proposed entanglement monotones turned to be equivalent to the convex roof construction, which hence gains an operational meaning. Some examples are given to demonstrate the different cases.