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Title: One-shot yield-cost relations in general quantum resource theories
Authors: Takagi, Ryuji
Regula, Bartosz
Wilde, Mark M.
Keywords: Science::Physics
Issue Date: 2022
Source: Takagi, R., Regula, B. & Wilde, M. M. (2022). One-shot yield-cost relations in general quantum resource theories. PRX Quantum, 3(1), 010348-1-010348-33.
Project: NRF-NRFF2016-02 
Journal: PRX Quantum
Abstract: Although it is well known that the amount of resources that can be asymptotically distilled from a quantum state or channel does not exceed the resource cost needed to produce it, the corresponding relation in the non-asymptotic regime hitherto has not been well understood. Here, we establish a quantitative relation between the one-shot distillable resource yield and dilution cost in terms of transformation errors involved in these processes. Notably, our bound is applicable to quantum state and channel manipulation with respect to any type of quantum resource and any class of free transformations thereof, encompassing broad types of settings, including entanglement, quantum thermodynamics, and quantum communication. We also show that our techniques provide strong converse bounds relating the distillable resource and resource dilution cost in the asymptotic regime. Moreover, we introduce a class of channels that generalize twirling maps encountered in many resource theories, and by directly connecting it with resource quantification, we compute analytically several smoothed resource measures and improve our one-shot yield--cost bound in relevant theories. We use these operational insights to exactly evaluate important measures for various resource states in the resource theory of magic states.
ISSN: 2691-3399
DOI: 10.1103/PRXQuantum.3.010348
Schools: School of Physical and Mathematical Sciences 
Research Centres: Nanyang Quantum Hub
Rights: © 2022 the Authors. Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.
Fulltext Permission: open
Fulltext Availability: With Fulltext
Appears in Collections:SPMS Journal Articles

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