Randomness for quantum channels: Genericity of catalysis and quantum advantage of uniformness
Randomness can help one to implement quantum maps that cannot be realized in a deterministic fashion. Recently, it was discovered that explicitly treating a randomness source as a quantum system could double the efficiency as a catalyst for some tasks. In this work, we first show that every quantum...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
American Physical Society
2021-03-01
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| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.3.013218 |
| _version_ | 1827285767944142848 |
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| author | Seok Hyung Lie Hyunseok Jeong |
| author_facet | Seok Hyung Lie Hyunseok Jeong |
| author_sort | Seok Hyung Lie |
| collection | DOAJ |
| description | Randomness can help one to implement quantum maps that cannot be realized in a deterministic fashion. Recently, it was discovered that explicitly treating a randomness source as a quantum system could double the efficiency as a catalyst for some tasks. In this work, we first show that every quantum channel that can be implemented with a randomness source without leaking information to it must be a catalysis. For that purpose, we prove a new no-go theorem that generalizes the no-hiding theorem, the no-secret theorem that states no quantum information can be shared with other systems as a secret without leaking some information. Second, we show that nondegenerate catalysts should be used classically when no extra dimension is allowed, which leads to the fact that the quantum advantage of a catalytic process strictly comes from the uniformness of the randomness source. Finally, we discuss a method to circumvent the previous result that achieves quantum advantage with nondegenerate catalyst uniformized by employing extra work space. |
| first_indexed | 2024-04-24T10:20:10Z |
| format | Article |
| id | doaj.art-1818b6f958754146a9e38df274c63686 |
| institution | Directory Open Access Journal |
| issn | 2643-1564 |
| language | English |
| last_indexed | 2024-04-24T10:20:10Z |
| publishDate | 2021-03-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| spelling | doaj.art-1818b6f958754146a9e38df274c636862024-04-12T17:08:02ZengAmerican Physical SocietyPhysical Review Research2643-15642021-03-013101321810.1103/PhysRevResearch.3.013218Randomness for quantum channels: Genericity of catalysis and quantum advantage of uniformnessSeok Hyung LieHyunseok JeongRandomness can help one to implement quantum maps that cannot be realized in a deterministic fashion. Recently, it was discovered that explicitly treating a randomness source as a quantum system could double the efficiency as a catalyst for some tasks. In this work, we first show that every quantum channel that can be implemented with a randomness source without leaking information to it must be a catalysis. For that purpose, we prove a new no-go theorem that generalizes the no-hiding theorem, the no-secret theorem that states no quantum information can be shared with other systems as a secret without leaking some information. Second, we show that nondegenerate catalysts should be used classically when no extra dimension is allowed, which leads to the fact that the quantum advantage of a catalytic process strictly comes from the uniformness of the randomness source. Finally, we discuss a method to circumvent the previous result that achieves quantum advantage with nondegenerate catalyst uniformized by employing extra work space.http://doi.org/10.1103/PhysRevResearch.3.013218 |
| spellingShingle | Seok Hyung Lie Hyunseok Jeong Randomness for quantum channels: Genericity of catalysis and quantum advantage of uniformness Physical Review Research |
| title | Randomness for quantum channels: Genericity of catalysis and quantum advantage of uniformness |
| title_full | Randomness for quantum channels: Genericity of catalysis and quantum advantage of uniformness |
| title_fullStr | Randomness for quantum channels: Genericity of catalysis and quantum advantage of uniformness |
| title_full_unstemmed | Randomness for quantum channels: Genericity of catalysis and quantum advantage of uniformness |
| title_short | Randomness for quantum channels: Genericity of catalysis and quantum advantage of uniformness |
| title_sort | randomness for quantum channels genericity of catalysis and quantum advantage of uniformness |
| url | http://doi.org/10.1103/PhysRevResearch.3.013218 |
| work_keys_str_mv | AT seokhyunglie randomnessforquantumchannelsgenericityofcatalysisandquantumadvantageofuniformness AT hyunseokjeong randomnessforquantumchannelsgenericityofcatalysisandquantumadvantageofuniformness |