On the complementary quantum capacity of the depolarizing channel
The qubit depolarizing channel with noise parameter $\eta$ transmits an input qubit perfectly with probability $1-\eta$, and outputs the completely mixed state with probability $\eta$. We show that its complementary channel has positive quantum capacity for all $\eta\gt 0$. Thus, we find that there...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften
2017-09-01
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| Series: | Quantum |
| Online Access: | https://quantum-journal.org/q-2017-09-19-28/pdf/ |
| _version_ | 1818297633542766592 |
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| author | Debbie Leung John Watrous |
| author_facet | Debbie Leung John Watrous |
| author_sort | Debbie Leung |
| collection | DOAJ |
| description | The qubit depolarizing channel with noise parameter $\eta$ transmits an input qubit perfectly with probability $1-\eta$, and outputs the completely mixed state with probability $\eta$. We show that its complementary channel has positive quantum capacity for all $\eta\gt 0$. Thus, we find that there exists a single parameter family of channels having the peculiar property of having positive quantum capacity even when the outputs of these channels approach a fixed state independent of the input. Comparisons with other related channels, and implications on the difficulty of studying the quantum capacity of the depolarizing channel are discussed. |
| first_indexed | 2024-12-13T04:22:32Z |
| format | Article |
| id | doaj.art-f4e11e93c2004bb79bffcef46b0f0b6d |
| institution | Directory Open Access Journal |
| issn | 2521-327X |
| language | English |
| last_indexed | 2024-12-13T04:22:32Z |
| publishDate | 2017-09-01 |
| publisher | Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften |
| record_format | Article |
| series | Quantum |
| spelling | doaj.art-f4e11e93c2004bb79bffcef46b0f0b6d2022-12-21T23:59:45ZengVerein zur Förderung des Open Access Publizierens in den QuantenwissenschaftenQuantum2521-327X2017-09-0112810.22331/q-2017-09-19-2810.22331/q-2017-09-19-28On the complementary quantum capacity of the depolarizing channelDebbie LeungJohn WatrousThe qubit depolarizing channel with noise parameter $\eta$ transmits an input qubit perfectly with probability $1-\eta$, and outputs the completely mixed state with probability $\eta$. We show that its complementary channel has positive quantum capacity for all $\eta\gt 0$. Thus, we find that there exists a single parameter family of channels having the peculiar property of having positive quantum capacity even when the outputs of these channels approach a fixed state independent of the input. Comparisons with other related channels, and implications on the difficulty of studying the quantum capacity of the depolarizing channel are discussed.https://quantum-journal.org/q-2017-09-19-28/pdf/ |
| spellingShingle | Debbie Leung John Watrous On the complementary quantum capacity of the depolarizing channel Quantum |
| title | On the complementary quantum capacity of the depolarizing channel |
| title_full | On the complementary quantum capacity of the depolarizing channel |
| title_fullStr | On the complementary quantum capacity of the depolarizing channel |
| title_full_unstemmed | On the complementary quantum capacity of the depolarizing channel |
| title_short | On the complementary quantum capacity of the depolarizing channel |
| title_sort | on the complementary quantum capacity of the depolarizing channel |
| url | https://quantum-journal.org/q-2017-09-19-28/pdf/ |
| work_keys_str_mv | AT debbieleung onthecomplementaryquantumcapacityofthedepolarizingchannel AT johnwatrous onthecomplementaryquantumcapacityofthedepolarizingchannel |