Ultimate limits of approximate unambiguous discrimination
Quantum hypothesis testing is an important tool for quantum information processing. Two main strategies have been widely adopted: in a minimum error discrimination strategy, the average error probability is minimized; while in an unambiguous discrimination strategy, an inconclusive decision (abstent...
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| Format: | Article |
| Language: | English |
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American Physical Society
2020-11-01
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| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.2.043276 |
| _version_ | 1827285892889313280 |
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| author | Quntao Zhuang |
| author_facet | Quntao Zhuang |
| author_sort | Quntao Zhuang |
| collection | DOAJ |
| description | Quantum hypothesis testing is an important tool for quantum information processing. Two main strategies have been widely adopted: in a minimum error discrimination strategy, the average error probability is minimized; while in an unambiguous discrimination strategy, an inconclusive decision (abstention) is allowed to vanish any possibility of errors when a conclusive result is obtained. In both scenarios, the testing between quantum states is relatively well understood, for example, the ultimate limits of the performance are established decades ago; however, the testing between quantum channels is less understood. Although the ultimate limit of minimum error discrimination between channels has been explored recently, the corresponding limit of unambiguous discrimination is unknown. In this paper, we formulate an approximate unambiguous discrimination scenario, and derive the ultimate limits of the performance for both states and channels. In particular, in the channel case, our lower bound of the inconclusive probability holds for arbitrary adaptive sensing protocols. For the special class of “teleportation-covariant” channels, the lower bound is achievable with maximum entangled inputs and no adaptive strategy is necessary. |
| first_indexed | 2024-04-24T10:22:17Z |
| format | Article |
| id | doaj.art-0d8a997fd87d4dd88f44349797b3dc5a |
| institution | Directory Open Access Journal |
| issn | 2643-1564 |
| language | English |
| last_indexed | 2024-04-24T10:22:17Z |
| publishDate | 2020-11-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| spelling | doaj.art-0d8a997fd87d4dd88f44349797b3dc5a2024-04-12T17:04:20ZengAmerican Physical SocietyPhysical Review Research2643-15642020-11-012404327610.1103/PhysRevResearch.2.043276Ultimate limits of approximate unambiguous discriminationQuntao ZhuangQuantum hypothesis testing is an important tool for quantum information processing. Two main strategies have been widely adopted: in a minimum error discrimination strategy, the average error probability is minimized; while in an unambiguous discrimination strategy, an inconclusive decision (abstention) is allowed to vanish any possibility of errors when a conclusive result is obtained. In both scenarios, the testing between quantum states is relatively well understood, for example, the ultimate limits of the performance are established decades ago; however, the testing between quantum channels is less understood. Although the ultimate limit of minimum error discrimination between channels has been explored recently, the corresponding limit of unambiguous discrimination is unknown. In this paper, we formulate an approximate unambiguous discrimination scenario, and derive the ultimate limits of the performance for both states and channels. In particular, in the channel case, our lower bound of the inconclusive probability holds for arbitrary adaptive sensing protocols. For the special class of “teleportation-covariant” channels, the lower bound is achievable with maximum entangled inputs and no adaptive strategy is necessary.http://doi.org/10.1103/PhysRevResearch.2.043276 |
| spellingShingle | Quntao Zhuang Ultimate limits of approximate unambiguous discrimination Physical Review Research |
| title | Ultimate limits of approximate unambiguous discrimination |
| title_full | Ultimate limits of approximate unambiguous discrimination |
| title_fullStr | Ultimate limits of approximate unambiguous discrimination |
| title_full_unstemmed | Ultimate limits of approximate unambiguous discrimination |
| title_short | Ultimate limits of approximate unambiguous discrimination |
| title_sort | ultimate limits of approximate unambiguous discrimination |
| url | http://doi.org/10.1103/PhysRevResearch.2.043276 |
| work_keys_str_mv | AT quntaozhuang ultimatelimitsofapproximateunambiguousdiscrimination |