Entanglement Breaking Rank via Complementary Channels and Multiplicative Domains

TL;DR

This paper introduces a novel method using multiplicative domains of complementary channels to determine if a quantum channel is entanglement breaking and to evaluate its entanglement breaking rank, providing new insights into quantum entanglement analysis.

Contribution

It presents a new technique based on multiplicative domains to analyze entanglement breaking channels and characterizes channels with projection Choi matrices.

Findings

Entanglement breaking and Choi ranks are equal for channels with projection Choi matrices.

A full description of entanglement breaking channels with projection Choi matrices is provided.

The introduced method offers a new way to evaluate entanglement breaking rank.

Abstract

Quantum entanglement can be studied through the theory of completely positive maps in a number of ways, including by making use of the Choi-Jamilkowski isomorphism, which identifies separable states with entanglement breaking quantum channels, and optimal ensemble length with entanglement breaking rank. The multiplicative domain is an important operator structure in the theory of completely positive maps. We introduce a new technique to determine if a channel is entanglement breaking and to evaluate entanglement breaking rank, based on an analysis of multiplicative domains determined by complementary quantum channels. We give a full description of the class of entanglement breaking channels that have a projection as their Choi matrix, and we show the entanglement breaking and Choi ranks of such channels are equal.