One-shot manipulation of entanglement for quantum channels

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.

arXiv comment19 pages, 5 figures. See two independent related works by B. Regula and R. Takagi, and by X. Yuan et al

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• Catalysis of entanglement and other quantum resources
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• Relation between Quantum Coherence and Quantum Entanglement in Quantum Measurements
• The Dynamical Resource Theory of Informational Non-Equilibrium
• Black Box Work Extraction and Composite Hypothesis Testing
• One-shot manipulation of coherence in dynamic quantum resource theory
• Projective robustness for quantum channels and measurements and their operational significance
• One-Shot Static Entanglement Cost of Bipartite Quantum Channels
• Single-shot entanglement manipulation of states and channels revisited