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dc.contributor.authorTakagi, Ryujien_US
dc.contributor.authorRegula, Bartoszen_US
dc.contributor.authorWilde, Mark M.en_US
dc.identifier.citationTakagi, 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.
dc.description.abstractAlthough 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.en_US
dc.description.sponsorshipMinistry of Education (MOE)en_US
dc.description.sponsorshipNanyang Technological Universityen_US
dc.description.sponsorshipNational Research Foundation (NRF)en_US
dc.relation.ispartofPRX Quantumen_US
dc.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.en_US
dc.titleOne-shot yield-cost relations in general quantum resource theoriesen_US
dc.typeJournal Articleen
dc.contributor.schoolSchool of Physical and Mathematical Sciencesen_US
dc.contributor.researchNanyang Quantum Huben_US
dc.description.versionPublished versionen_US
dc.subject.keywordsCorresponding Relationsen_US
dc.description.acknowledgementR.T. acknowledges the support from the National Research Foundation (NRF), Singapore, under its NRFF Fellow program (Award No. NRF-NRFF2016- 02), the Singapore Ministry of Education Tier 1 Grant No. 2019-T1-002-015, and the Lee Kuan Yew Postdoctoral Fellowship at Nanyang Technological University Singapore. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not reflect the views of the National Research Foundation, Singapore. B.R. acknowledges the support of the Japan Society for the Promotion of Science (JSPS) KAKENHI Grant No. 21F21015, the JSPS Postdoctoral Fellowship for Research in Japan, and the Presidential Postdoctoral Fellowship from Nanyang Technological University, Singapore. M.M.W. acknowledges support from the NSF under Grant No. 1907615.en_US
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