One-Shot Static Entanglement Cost of Bipartite Quantum Channels

TL;DR

This paper explores the minimal entanglement needed to simulate bipartite quantum channels in a one-shot setting, establishing bounds based on robustness measures and extending the set of free channels to include superchannels.

Contribution

It introduces a new framework for quantifying one-shot static entanglement cost using robustness measures and extends the set of free channels to include superchannels, providing exact cost formulas.

Findings

Lower bound on entanglement cost via generalized robustness

Extended set of channels allows exact cost calculation with log-robustness

Extended channels set is equivalent to free superchannels

Abstract

We first investigate the one-shot static entanglement cost to simulate a bipartite quantum channel under the set of non-entangling channels. The lower bound on the static entanglement cost is given by the generalized robustness of the target channel as well as the robust-generating power of the channel, which implies that the cost necessary to generate a bipartite quantum channel might not be retrievable in general. Next, we conceive a set of quantum channels that extends the set of non-entangling channels. We find out that the one-shot static entanglement cost under the extended set of channels is given by the channel's standard log-robustness. This gives the one-shot dynamic entanglement cost under a set of free superchannels that do not generate dynamic entanglement resource; the extended set is shown to be equivalent to the set of free superchannels.