Quantifying Entanglement with Coherence

TL;DR

This paper introduces a new measure called entanglement coherence that quantifies bipartite pure state entanglement by linking it to quantum coherence in the Schmidt basis, revealing deep connections between entanglement, coherence, and skew information.

Contribution

It proposes a novel entanglement measure based on coherence in the Schmidt basis, connecting entanglement to quantum coherence and skew information.

Findings

Entanglement coherence equals 1 for maximally entangled states.

Entanglement coherence is 0 for separable states.

It relates to the unified entropy and Wigner-Yanase skew information.

Abstract

Quantifying entanglement is a work in progress which is important for the active field of quantum information and computation. A measure of bipartite pure state entanglement is proposed here, named entanglement coherence, which is essentially the normalized coherence of the entangled state in its Schmidt basis. Its value is 1 for maximally entangled states, and 0 for separable states, irrespective of the dimensionality of the Hilbert space. So a maximally entangled state is also the one which is maximally coherent in its Schmidt basis. Quantum entanglement and quantum coherence are thus intimately connected. Entanglement coherence turns out to be closely related to the unified entropy of the reduced state of one of the subsystems. Additionally it is shown that the entanglement coherence is closely connected to the Wigner-Yanase skew information of the reduced density operator of one of the subsystems, in an interesting way.