Nullspaces of Entanglement Breaking Channels and Applications

TL;DR

This paper explores the nullspace structures of entanglement breaking channels, providing new insights into their properties, tests for mixed unitarity, and conditions for private algebra existence, with implications for quantum information theory.

Contribution

It demonstrates that any trace-zero operator space can be realized as a nullspace of an entanglement breaking channel and introduces a test for mixed unitarity based on nullspace analysis.

Findings

Any trace-zero operator space is the nullspace of an entanglement breaking channel

A new test for mixed unitarity using complementary channel behavior

Conditions established for the existence of private algebras in certain channels

Abstract

We investigate the nullspace structures of entanglement breaking channels, and related applications. We show that every operator space of trace zero matrices is the nullspace of an entanglement breaking channel. We derive a test for mixed unitarity of quantum channels based on complementary channel behaviour and entanglement breaking channel nullspaces. We identify conditions that guarantee the existence of private algebras for certain classes of entanglement breaking channels.