Entanglement-breaking superchannels

TL;DR

This paper introduces and characterizes entanglement-breaking superchannels, exploring their properties, implementations, and limitations, including superactivation phenomena and the concept of (p,q)-non-entangling channels, advancing the understanding of quantum channel transformations.

Contribution

It provides the first comprehensive study of entanglement-breaking superchannels, including their characterizations, superactivation, and the introduction of (p,q)-non-entangling channels, revealing fundamental differences from channels.

Findings

Not all EB superchannels can be implemented as measure-and-prepare.

Many EB superchannels can be superactivated to produce non-separable channels.

Introduction of (p,q)-non-entangling channels and examples of (p,q)-EB superchannels.

Abstract

In this paper we initiate the study of entanglement-breaking (EB) superchannels. These are processes that always yield separable maps when acting on one side of a bipartite completely positive (CP) map. EB superchannels are a generalization of the well-known EB channels. We give several equivalent characterizations of EB supermaps and superchannels. Unlike its channel counterpart, we find that not every EB superchannel can be implemented as a measure-and-prepare superchannel. We also demonstrate that many EB superchannels can be superactivated, in the sense that they can output non-separable channels when wired in series. We then introduce the notions of CPTP- and CP-complete images of a superchannel, which capture deterministic and probabilistic channel convertibility, respectively. This allows us to characterize the power of EB superchannels for generating CP maps in different scenarios, and it reveals some fundamental differences between channels and superchannels. Finally, we relax the definition of separable channels to include (p,q)-non-entangling channels, which are bipartite channels that cannot generate entanglement using p- and q-dimensional ancillary systems. By introducing and investigating k-EB maps, we construct examples of (p,q)-EB superchannels that are not fully entanglement breaking. Partial results on the characterization of (p,q)-EB superchannels are also provided.