One-shot manipulation of entanglement for quantum channels

TL;DR

This paper formulates the dynamic resource theory of quantum entanglement using superchannel theory, establishing bounds on entanglement cost and distillation for bipartite quantum channels.

Contribution

It introduces a superchannel-based framework for dynamic entanglement and derives bounds on one-shot entanglement cost and distillation using resource monotones.

Findings

Bound on one-shot dynamic entanglement cost using log-robustness.

Bound on one-shot distillable dynamic entanglement using hypothesis-testing relative entropy.

Analysis of catalytic dynamic entanglement cost with generalized robustness.

Abstract

We show that the dynamic resource theory of quantum entanglement can be formulated using the superchannel theory. In this formulation, we identify the separable channels and the class of free superchannels that preserve channel separability as free resources, and choose the swap channels as dynamic entanglement golden units. Our first result is that the one-shot dynamic entanglement cost of a bipartite quantum channel under the free superchannels is bounded by the standard log-robustness of channels. The one-shot distillable dynamic entanglement of a bipartite quantum channel under the free superchannels is found to be bounded by a resource monotone that we construct from the hypothesis-testing relative entropy of channels with minimization over separable channels. We also address the one-shot catalytic dynamic entanglement cost of a bipartite quantum channel under a larger class of free superchannels that could generate the dynamic entanglement which is asymptotically negligible; it is bounded by the generalized log-robustness of channels.