Additive Classical Capacity of Quantum Channels Assisted by Noisy Entanglement
We give a capacity formula for the classical information transmission over a noisy quantum channel, with separable encoding by the sender and limited resources provided by the receiver’s preshared ancilla. Instead of a pure state, we consider the signal-ancilla pair in a mixed state, purified by a “...
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| Format: | Article |
| Language: | English |
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American Physical Society
2017
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| Online Access: | http://hdl.handle.net/1721.1/109828 https://orcid.org/0000-0002-9554-3846 https://orcid.org/0000-0002-4497-2093 https://orcid.org/0000-0003-4626-5648 |
| _version_ | 1826198789906497536 |
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| author | Zhuang, Quntao Zhu, Elton Shor, Peter Williston |
| author2 | Massachusetts Institute of Technology. Center for Theoretical Physics |
| author_facet | Massachusetts Institute of Technology. Center for Theoretical Physics Zhuang, Quntao Zhu, Elton Shor, Peter Williston |
| author_sort | Zhuang, Quntao |
| collection | MIT |
| description | We give a capacity formula for the classical information transmission over a noisy quantum channel, with separable encoding by the sender and limited resources provided by the receiver’s preshared ancilla. Instead of a pure state, we consider the signal-ancilla pair in a mixed state, purified by a “witness.” Thus, the signal-witness correlation limits the resource available from the signal-ancilla correlation. Our formula characterizes the utility of different forms of resources, including noisy or limited entanglement assistance, for classical communication. With separable encoding, the sender’s signals across multiple channel uses are still allowed to be entangled, yet our capacity formula is additive. In particular, for generalized covariant channels, our capacity formula has a simple closed form. Moreover, our additive capacity formula upper bounds the general coherent attack’s information gain in various two-way quantum key distribution protocols. For Gaussian protocols, the additivity of the formula indicates that the collective Gaussian attack is the most powerful. |
| first_indexed | 2024-09-23T11:09:43Z |
| format | Article |
| id | mit-1721.1/109828 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T11:09:43Z |
| publishDate | 2017 |
| publisher | American Physical Society |
| record_format | dspace |
| spelling | mit-1721.1/1098282022-10-01T01:45:23Z Additive Classical Capacity of Quantum Channels Assisted by Noisy Entanglement Zhuang, Quntao Zhu, Elton Shor, Peter Williston Massachusetts Institute of Technology. Center for Theoretical Physics Massachusetts Institute of Technology. Department of Mathematics Massachusetts Institute of Technology. Department of Physics Massachusetts Institute of Technology. Research Laboratory of Electronics Zhuang, Quntao Zhu, Elton Shor, Peter Williston We give a capacity formula for the classical information transmission over a noisy quantum channel, with separable encoding by the sender and limited resources provided by the receiver’s preshared ancilla. Instead of a pure state, we consider the signal-ancilla pair in a mixed state, purified by a “witness.” Thus, the signal-witness correlation limits the resource available from the signal-ancilla correlation. Our formula characterizes the utility of different forms of resources, including noisy or limited entanglement assistance, for classical communication. With separable encoding, the sender’s signals across multiple channel uses are still allowed to be entangled, yet our capacity formula is additive. In particular, for generalized covariant channels, our capacity formula has a simple closed form. Moreover, our additive capacity formula upper bounds the general coherent attack’s information gain in various two-way quantum key distribution protocols. For Gaussian protocols, the additivity of the formula indicates that the collective Gaussian attack is the most powerful. United States. Air Force. Office of Scientific Research (Grant FA9550-14-1-0052) Massachusetts Institute of Technology. Research Laboratory of Electronics (Claude E. Shannon Fellowship) National Science Foundation (U.S.) (Grant CCF-1525130) National Science Foundation (U.S.) (Center for Science of Information. Grant CCF0-939370) 2017-06-13T18:14:23Z 2017-06-13T18:14:23Z 2017-05 2016-10 2017-05-19T22:00:04Z Article http://purl.org/eprint/type/JournalArticle 0031-9007 1079-7114 http://hdl.handle.net/1721.1/109828 Zhuang, Quntao, Elton Yechao Zhu, and Peter W. Shor. “Additive Classical Capacity of Quantum Channels Assisted by Noisy Entanglement.” Physical Review Letters 118.20 (2017): n. pag. © 2017 American Physical Society https://orcid.org/0000-0002-9554-3846 https://orcid.org/0000-0002-4497-2093 https://orcid.org/0000-0003-4626-5648 en http://dx.doi.org/10.1103/PhysRevLett.118.200503 Physical Review Letters Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. American Physical Society application/pdf American Physical Society American Physical Society |
| spellingShingle | Zhuang, Quntao Zhu, Elton Shor, Peter Williston Additive Classical Capacity of Quantum Channels Assisted by Noisy Entanglement |
| title | Additive Classical Capacity of Quantum Channels Assisted by Noisy Entanglement |
| title_full | Additive Classical Capacity of Quantum Channels Assisted by Noisy Entanglement |
| title_fullStr | Additive Classical Capacity of Quantum Channels Assisted by Noisy Entanglement |
| title_full_unstemmed | Additive Classical Capacity of Quantum Channels Assisted by Noisy Entanglement |
| title_short | Additive Classical Capacity of Quantum Channels Assisted by Noisy Entanglement |
| title_sort | additive classical capacity of quantum channels assisted by noisy entanglement |
| url | http://hdl.handle.net/1721.1/109828 https://orcid.org/0000-0002-9554-3846 https://orcid.org/0000-0002-4497-2093 https://orcid.org/0000-0003-4626-5648 |
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