The noisy Landau-Streater(Werner-Holevo) channel in arbitrary dimensions
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866918189368082432 |
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| author | Karimipour, Vahid |
| author_facet | Karimipour, Vahid |
| contents | Two important classes of quantum channels, namly the Werner-Holevo and the Landau-Streater channels are known to be related only in three dimensions, i.e. when acting on qutrits. In this work, definition of the Landau-Streater channel is extended in such a way which retains its equivalence to the Werner-Holevo channel in all dimensions. This channel is then modified to be representable as a model of noise acting on qudits. We then investigate propeties of the resulting noisy channel and determine the conditions under which it cannot be the result of a Markovian evolution. Furthermore, we investigate its different capacities for transmitting classical and quantum information with or without entanglement. In particular, while the pure (or high noise) Landau-Streater or the Werner-Holevo channel is entanglement breaking and hence has zero capacity, by finding a lower bound for the quantum capacity, we show that when the level of noise is lower than a critical value the quantum capacity will be non-zero. Surprizingly this value turns out to be approximately equal to $0.4$ in all dimensions. Finally we show that, in even dimension, this channel has a decomposition in terms of unitary operations. This is in contrast with the three dimensional case where it has been proved that such a decomposition is impossible, even in terms of other quantum maps. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_07700 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The noisy Landau-Streater(Werner-Holevo) channel in arbitrary dimensions Karimipour, Vahid Quantum Physics Mathematical Physics Two important classes of quantum channels, namly the Werner-Holevo and the Landau-Streater channels are known to be related only in three dimensions, i.e. when acting on qutrits. In this work, definition of the Landau-Streater channel is extended in such a way which retains its equivalence to the Werner-Holevo channel in all dimensions. This channel is then modified to be representable as a model of noise acting on qudits. We then investigate propeties of the resulting noisy channel and determine the conditions under which it cannot be the result of a Markovian evolution. Furthermore, we investigate its different capacities for transmitting classical and quantum information with or without entanglement. In particular, while the pure (or high noise) Landau-Streater or the Werner-Holevo channel is entanglement breaking and hence has zero capacity, by finding a lower bound for the quantum capacity, we show that when the level of noise is lower than a critical value the quantum capacity will be non-zero. Surprizingly this value turns out to be approximately equal to $0.4$ in all dimensions. Finally we show that, in even dimension, this channel has a decomposition in terms of unitary operations. This is in contrast with the three dimensional case where it has been proved that such a decomposition is impossible, even in terms of other quantum maps. |
| title | The noisy Landau-Streater(Werner-Holevo) channel in arbitrary dimensions |
| topic | Quantum Physics Mathematical Physics |
| url | https://arxiv.org/abs/2402.07700 |