Relating Entropies of Quantum Channels
In this work, we study two different approaches to defining the entropy of a quantum channel. One of these is based on the von Neumann entropy of the corresponding Choi–Jamiołkowski state. The second one is based on the relative entropy of the output of the extended channel relative to the output of...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-08-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/23/8/1028 |
| _version_ | 1827685240688082944 |
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| author | Dariusz Kurzyk Łukasz Pawela Zbigniew Puchała |
| author_facet | Dariusz Kurzyk Łukasz Pawela Zbigniew Puchała |
| author_sort | Dariusz Kurzyk |
| collection | DOAJ |
| description | In this work, we study two different approaches to defining the entropy of a quantum channel. One of these is based on the von Neumann entropy of the corresponding Choi–Jamiołkowski state. The second one is based on the relative entropy of the output of the extended channel relative to the output of the extended completely depolarizing channel. This entropy then needs to be optimized over all possible input states. Our results first show that the former entropy provides an upper bound on the latter. Next, we show that for unital qubit channels, this bound is saturated. Finally, we conjecture and provide numerical intuitions that the bound can also be saturated for random channels as their dimension tends to infinity. |
| first_indexed | 2024-03-10T08:50:02Z |
| format | Article |
| id | doaj.art-bc96f4b4c93c4e9e9f8a13c8bb8f6217 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-10T08:50:02Z |
| publishDate | 2021-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-bc96f4b4c93c4e9e9f8a13c8bb8f62172023-11-22T07:35:14ZengMDPI AGEntropy1099-43002021-08-01238102810.3390/e23081028Relating Entropies of Quantum ChannelsDariusz Kurzyk0Łukasz Pawela1Zbigniew Puchała2Institute of Theoretical and Applied Informatics, Polish Academy of Sciences, ul. Bałtycka 5, 44-100 Gliwice, PolandInstitute of Theoretical and Applied Informatics, Polish Academy of Sciences, ul. Bałtycka 5, 44-100 Gliwice, PolandInstitute of Theoretical and Applied Informatics, Polish Academy of Sciences, ul. Bałtycka 5, 44-100 Gliwice, PolandIn this work, we study two different approaches to defining the entropy of a quantum channel. One of these is based on the von Neumann entropy of the corresponding Choi–Jamiołkowski state. The second one is based on the relative entropy of the output of the extended channel relative to the output of the extended completely depolarizing channel. This entropy then needs to be optimized over all possible input states. Our results first show that the former entropy provides an upper bound on the latter. Next, we show that for unital qubit channels, this bound is saturated. Finally, we conjecture and provide numerical intuitions that the bound can also be saturated for random channels as their dimension tends to infinity.https://www.mdpi.com/1099-4300/23/8/1028quantum channelsrandom matricesentropies of quantum states |
| spellingShingle | Dariusz Kurzyk Łukasz Pawela Zbigniew Puchała Relating Entropies of Quantum Channels Entropy quantum channels random matrices entropies of quantum states |
| title | Relating Entropies of Quantum Channels |
| title_full | Relating Entropies of Quantum Channels |
| title_fullStr | Relating Entropies of Quantum Channels |
| title_full_unstemmed | Relating Entropies of Quantum Channels |
| title_short | Relating Entropies of Quantum Channels |
| title_sort | relating entropies of quantum channels |
| topic | quantum channels random matrices entropies of quantum states |
| url | https://www.mdpi.com/1099-4300/23/8/1028 |
| work_keys_str_mv | AT dariuszkurzyk relatingentropiesofquantumchannels AT łukaszpawela relatingentropiesofquantumchannels AT zbigniewpuchała relatingentropiesofquantumchannels |