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 usingp- andq-dimensional ancillary systems. By introducing and investigatingk-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.
Highlights
Suppose that Alice and Rachel have access to some bipartite quantum channel EA0R0→A1R1
We introduce the Werner states [33] which will play an important role in our construction of k-entanglementbreaking channels (EBCs)
While left open the question whether every Entanglement-breaking superchannels (EBSCs) can be implemented with partly-entanglement breaking (EB) pre/post-processing channels, we show that a generic implementation must allow entangling the input system to the memory system of a superchannel
Summary
Suppose that Alice and Rachel have access to some bipartite quantum channel EA0R0→A1R1. Frustrated with the situation, Alice naively wonders if manipulating her part of the channel could improve their prospects of obtaining entanglement Any physical procedure she attempts can be described as in Fig. 2; it involves her first applying some preprocessing map that couples her input system A0 to the memory register AE, and applying a post-processing map to system AE and her channel output A1 [2]. This begs the question of whether there exist certain local superchannels for Alice that convert every bipartite channel into a separable channel We refer to such processes as entanglement-breaking superchannels since they completely eliminate any channel’s ability to distribute entanglement, and they are the focus of this paper.
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