Fidelity and Fisher information on quantum channels
The fidelity function for quantum states has been widely used in quantum information science and frequently arises in the quantification of optimal performances for the estimation and distinguishing of quantum states. A fidelity function for quantum channels is expected to have the same wide applica...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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IOP Publishing
2017-01-01
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| Series: | New Journal of Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1088/1367-2630/aa874c |
| _version_ | 1827873354336436224 |
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| author | Haidong Yuan Chi-Hang Fred Fung |
| author_facet | Haidong Yuan Chi-Hang Fred Fung |
| author_sort | Haidong Yuan |
| collection | DOAJ |
| description | The fidelity function for quantum states has been widely used in quantum information science and frequently arises in the quantification of optimal performances for the estimation and distinguishing of quantum states. A fidelity function for quantum channels is expected to have the same wide applications in quantum information science. In this paper we propose a fidelity function for quantum channels and show that various distance measures on quantum channels can be obtained from this fidelity function; for example, the Bures angle and the Bures distance can be extended to quantum channels via this fidelity function. We then show that the distances between quantum channels lead naturally to a quantum channel Fisher information which quantifies the ultimate precision limit in quantum metrology; the ultimate precision limit can thus be seen as a manifestation of the distances between quantum channels. We also show that the fidelity of quantum channels provides a unified framework for perfect quantum channel discrimination and quantum metrology. In particular, we show that the minimum number of uses needed for perfect channel discrimination is exactly the counterpart of the precision limit in quantum metrology, and various useful lower bounds for the minimum number of uses needed for perfect channel discrimination can be obtained via this connection. |
| first_indexed | 2024-03-12T16:35:50Z |
| format | Article |
| id | doaj.art-c13c774c0bab41fe823a0fe67d9ba155 |
| institution | Directory Open Access Journal |
| issn | 1367-2630 |
| language | English |
| last_indexed | 2024-03-12T16:35:50Z |
| publishDate | 2017-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | New Journal of Physics |
| spelling | doaj.art-c13c774c0bab41fe823a0fe67d9ba1552023-08-08T14:54:46ZengIOP PublishingNew Journal of Physics1367-26302017-01-01191111303910.1088/1367-2630/aa874cFidelity and Fisher information on quantum channelsHaidong Yuan0Chi-Hang Fred Fung1Department of Mechanical and Automation Engineering, The Chinese University of Hong Kong , Shatin, Hong KongGerman Research Center, Huawei Technologies Düsseldorf GmbH , Munich, GermanyThe fidelity function for quantum states has been widely used in quantum information science and frequently arises in the quantification of optimal performances for the estimation and distinguishing of quantum states. A fidelity function for quantum channels is expected to have the same wide applications in quantum information science. In this paper we propose a fidelity function for quantum channels and show that various distance measures on quantum channels can be obtained from this fidelity function; for example, the Bures angle and the Bures distance can be extended to quantum channels via this fidelity function. We then show that the distances between quantum channels lead naturally to a quantum channel Fisher information which quantifies the ultimate precision limit in quantum metrology; the ultimate precision limit can thus be seen as a manifestation of the distances between quantum channels. We also show that the fidelity of quantum channels provides a unified framework for perfect quantum channel discrimination and quantum metrology. In particular, we show that the minimum number of uses needed for perfect channel discrimination is exactly the counterpart of the precision limit in quantum metrology, and various useful lower bounds for the minimum number of uses needed for perfect channel discrimination can be obtained via this connection.https://doi.org/10.1088/1367-2630/aa874cquantum metrologyFisher informationquantum information |
| spellingShingle | Haidong Yuan Chi-Hang Fred Fung Fidelity and Fisher information on quantum channels New Journal of Physics quantum metrology Fisher information quantum information |
| title | Fidelity and Fisher information on quantum channels |
| title_full | Fidelity and Fisher information on quantum channels |
| title_fullStr | Fidelity and Fisher information on quantum channels |
| title_full_unstemmed | Fidelity and Fisher information on quantum channels |
| title_short | Fidelity and Fisher information on quantum channels |
| title_sort | fidelity and fisher information on quantum channels |
| topic | quantum metrology Fisher information quantum information |
| url | https://doi.org/10.1088/1367-2630/aa874c |
| work_keys_str_mv | AT haidongyuan fidelityandfisherinformationonquantumchannels AT chihangfredfung fidelityandfisherinformationonquantumchannels |