Maximal Entanglement - A New Measure of Entanglement

TL;DR

This paper introduces maximal entanglement, a new measure derived from maximal correlation, which effectively quantifies entanglement by being faithful, monotone under local operations, and consistent across tensor powers.

Contribution

It defines a novel entanglement measure based on maximal correlation, extending its properties to bipartite quantum states and demonstrating its key features.

Findings

Maximal entanglement is zero for separable states.

It is positive for entangled states.

The measure remains consistent on tensor powers.

Abstract

Maximal correlation is a measure of correlation for bipartite distributions. This measure has two intriguing features: (1) it is monotone under local stochastic maps; (2) it gives the same number when computed on i.i.d. copies of a pair of random variables. This measure of correlation has recently been generalized for bipartite quantum states, for which the same properties have been proved. In this paper, based on maximal correlation, we define a new measure of entanglement which we call maximal entanglement. We show that this measure of entanglement is faithful (is zero on separable states and positive on entangled states), is monotone under local quantum operations, and gives the same number when computed on tensor powers of a bipartite state.