One-Shot Operational Quantum Resource Theory

A fundamental approach for the characterization and quantification of all kinds of resources is to study the conversion between different resource objects under certain constraints. Here we analyze, from a resource-nonspecific standpoint, the optimal efficiency of resource formation and distillation...

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Bibliographic Details
Published in:Physical review letters 2019-07, Vol.123 (2), p.020401-020401, Article 020401
Main Authors: Liu, Zi-Wen, Bu, Kaifeng, Takagi, Ryuji
Format: Article
Language:English
Subjects:
Conversion
Distillation
Entanglement
Superposition (mathematics)
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Summary:A fundamental approach for the characterization and quantification of all kinds of resources is to study the conversion between different resource objects under certain constraints. Here we analyze, from a resource-nonspecific standpoint, the optimal efficiency of resource formation and distillation tasks with only a single copy of the given quantum state, thereby establishing a unified framework of one-shot quantum resource manipulation. We find general bounds on the optimal rates characterized by resource measures based on the smooth max- or min-relative entropies and hypothesis testing relative entropy, as well as the free robustness measure, providing them with general operational meanings in terms of optimal state conversion. Our results encompass a wide class of resource theories via the theory-dependent coefficients we introduce, and the discussions are solidified by important examples, such as entanglement, coherence, superposition, magic states, asymmetry, and thermal nonequilibrium.
ISSN:0031-9007
1079-7114
DOI:10.1103/physrevlett.123.020401