Partial order on passive states and Hoffman majorization in quantum thermodynamics
Passive states, i.e., those states from which no work can be extracted via unitary operations, play an important role in the foundations and applications of quantum thermodynamics. They generalize the familiar Gibbs thermal states, which are the sole passive states being stable under tensor product....
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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American Physical Society
2021-07-01
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| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.3.033091 |
| _version_ | 1797211010991390720 |
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| author | Uttam Singh Siddhartha Das Nicolas J. Cerf |
| author_facet | Uttam Singh Siddhartha Das Nicolas J. Cerf |
| author_sort | Uttam Singh |
| collection | DOAJ |
| description | Passive states, i.e., those states from which no work can be extracted via unitary operations, play an important role in the foundations and applications of quantum thermodynamics. They generalize the familiar Gibbs thermal states, which are the sole passive states being stable under tensor product. Here, we introduce a partial order on the set of passive states that captures the idea of a passive state being virtually cooler than another one. This partial order, which we build by defining the notion of relative passivity, offers a fine-grained comparison between passive states based on virtual temperatures (just like thermal states are compared based on their temperatures). We then characterize the quantum operations that are closed on the set of virtually cooler states with respect to some fixed input and output passive states. Viewing the activity, i.e., nonpassivity, of a state as a resource, our main result is then a necessary and sufficient condition on the transformation of a class of pure active states under these relative passivity-preserving operations. This condition gives a quantum thermodynamical meaning to the majorization relation on the set of nonincreasing vectors due to Hoffman. The maximum extractable work under relative passivity-preserving operations is then shown to be equal to the ergotropy of these pure active states. Finally, we are able to fully characterize passivity-preserving operations in the simpler case of qubit systems, and hence to derive a state interconversion condition under passivity-preserving qubit operations. The prospect of this work is a general resource-theoretical framework for the extractable work via quantum operations going beyond thermal operations. |
| first_indexed | 2024-04-24T10:19:42Z |
| format | Article |
| id | doaj.art-abc2bc529aca430c810c60a8ba0436c1 |
| institution | Directory Open Access Journal |
| issn | 2643-1564 |
| language | English |
| last_indexed | 2024-04-24T10:19:42Z |
| publishDate | 2021-07-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| spelling | doaj.art-abc2bc529aca430c810c60a8ba0436c12024-04-12T17:12:12ZengAmerican Physical SocietyPhysical Review Research2643-15642021-07-013303309110.1103/PhysRevResearch.3.033091Partial order on passive states and Hoffman majorization in quantum thermodynamicsUttam SinghSiddhartha DasNicolas J. CerfPassive states, i.e., those states from which no work can be extracted via unitary operations, play an important role in the foundations and applications of quantum thermodynamics. They generalize the familiar Gibbs thermal states, which are the sole passive states being stable under tensor product. Here, we introduce a partial order on the set of passive states that captures the idea of a passive state being virtually cooler than another one. This partial order, which we build by defining the notion of relative passivity, offers a fine-grained comparison between passive states based on virtual temperatures (just like thermal states are compared based on their temperatures). We then characterize the quantum operations that are closed on the set of virtually cooler states with respect to some fixed input and output passive states. Viewing the activity, i.e., nonpassivity, of a state as a resource, our main result is then a necessary and sufficient condition on the transformation of a class of pure active states under these relative passivity-preserving operations. This condition gives a quantum thermodynamical meaning to the majorization relation on the set of nonincreasing vectors due to Hoffman. The maximum extractable work under relative passivity-preserving operations is then shown to be equal to the ergotropy of these pure active states. Finally, we are able to fully characterize passivity-preserving operations in the simpler case of qubit systems, and hence to derive a state interconversion condition under passivity-preserving qubit operations. The prospect of this work is a general resource-theoretical framework for the extractable work via quantum operations going beyond thermal operations.http://doi.org/10.1103/PhysRevResearch.3.033091 |
| spellingShingle | Uttam Singh Siddhartha Das Nicolas J. Cerf Partial order on passive states and Hoffman majorization in quantum thermodynamics Physical Review Research |
| title | Partial order on passive states and Hoffman majorization in quantum thermodynamics |
| title_full | Partial order on passive states and Hoffman majorization in quantum thermodynamics |
| title_fullStr | Partial order on passive states and Hoffman majorization in quantum thermodynamics |
| title_full_unstemmed | Partial order on passive states and Hoffman majorization in quantum thermodynamics |
| title_short | Partial order on passive states and Hoffman majorization in quantum thermodynamics |
| title_sort | partial order on passive states and hoffman majorization in quantum thermodynamics |
| url | http://doi.org/10.1103/PhysRevResearch.3.033091 |
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