The Origin of Separable States and Separability Criteria from Entanglement-breaking Channels

TL;DR

This paper explores the relationship between separable states and entanglement-breaking channels, providing new criteria for determining separability based on channel properties.

Contribution

It introduces a novel perspective linking separable states to entanglement-breaking channels and derives new necessary and sufficient separability criteria.

Findings

Any separable state can be generated by an entanglement-breaking channel from a maximally entangled state.

Provides a necessary and sufficient criterion for separability.

Offers additional sufficient criteria for separability.

Abstract

In this paper, we show that an arbitrary separable state can be the output of a certain entanglement-breaking channel corresponding exactly to the input of a maximally entangled state. A necessary and sufficient separability criterion and some sufficient separability criteria from entanglement-breaking channels are given.