One-Shot Yield-Cost Relations in General Quantum Resource Theories
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 nonasymptotic regime hitherto has not been well understood. Here, we establish a quant...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
American Physical Society
2022-03-01
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| Series: | PRX Quantum |
| Online Access: | http://doi.org/10.1103/PRXQuantum.3.010348 |
| _version_ | 1828739913905864704 |
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| author | Ryuji Takagi Bartosz Regula Mark M. Wilde |
| author_facet | Ryuji Takagi Bartosz Regula Mark M. Wilde |
| author_sort | Ryuji Takagi |
| collection | DOAJ |
| description | 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 nonasymptotic 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 the resource dilution cost in the asymptotic regime. Moreover, we introduce a class of channels that generalize the 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. |
| first_indexed | 2024-04-13T00:30:48Z |
| format | Article |
| id | doaj.art-21a13336c6a94084922aef1d829ce1c6 |
| institution | Directory Open Access Journal |
| issn | 2691-3399 |
| language | English |
| last_indexed | 2024-04-13T00:30:48Z |
| publishDate | 2022-03-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | PRX Quantum |
| spelling | doaj.art-21a13336c6a94084922aef1d829ce1c62022-12-22T03:10:29ZengAmerican Physical SocietyPRX Quantum2691-33992022-03-013101034810.1103/PRXQuantum.3.010348One-Shot Yield-Cost Relations in General Quantum Resource TheoriesRyuji TakagiBartosz RegulaMark M. WildeAlthough 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 nonasymptotic 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 the resource dilution cost in the asymptotic regime. Moreover, we introduce a class of channels that generalize the 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.http://doi.org/10.1103/PRXQuantum.3.010348 |
| spellingShingle | Ryuji Takagi Bartosz Regula Mark M. Wilde One-Shot Yield-Cost Relations in General Quantum Resource Theories PRX Quantum |
| title | One-Shot Yield-Cost Relations in General Quantum Resource Theories |
| title_full | One-Shot Yield-Cost Relations in General Quantum Resource Theories |
| title_fullStr | One-Shot Yield-Cost Relations in General Quantum Resource Theories |
| title_full_unstemmed | One-Shot Yield-Cost Relations in General Quantum Resource Theories |
| title_short | One-Shot Yield-Cost Relations in General Quantum Resource Theories |
| title_sort | one shot yield cost relations in general quantum resource theories |
| url | http://doi.org/10.1103/PRXQuantum.3.010348 |
| work_keys_str_mv | AT ryujitakagi oneshotyieldcostrelationsingeneralquantumresourcetheories AT bartoszregula oneshotyieldcostrelationsingeneralquantumresourcetheories AT markmwilde oneshotyieldcostrelationsingeneralquantumresourcetheories |