Bipartite entanglement-annihilating maps: necessary and sufficient conditions

TL;DR

This paper fully characterizes bipartite entanglement-annihilating channels, providing necessary and sufficient conditions, operational criteria, and applications to noise models, crucial for avoiding entanglement destruction in quantum experiments.

Contribution

It introduces a complete characterization of entanglement-annihilating channels using positive maps and provides practical criteria for identifying such channels.

Findings

Derived criteria for EA channels with physical interpretation

Identified noise thresholds causing disentanglement in depolarizing channels

Discussed robustness of certain entangled states against noise

Abstract

We fully characterize bipartite entanglement-annihilating (EA) channels that destroy entanglement of any state shared by subsystems and, thus, should be avoided in any entanglement-enabled experiment. Our approach relies on extending the problem to EA positive maps, the cone of which remains invariant under concatenation with partially positive maps. Due to this invariancy, positive EA maps adopt a well characterization and their intersection with completely positive trace-preserving maps results in the set of EA channels. In addition to a general description, we also provide sufficient operational criteria revealing EA channels. They have a clear physical meaning since the processes involved contain stages of classical information transfer for subsystems. We demonstrate the applicability of derived criteria for local and global depolarizing noises, and specify corresponding noise levels beyond which any initial state becomes disentangled after passing the channel. The robustness of some entangled states is discussed.