Capacities of a two-parameter family of noisy Werner-Holevo channels
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909700337958912 |
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| author | Roofeh, Shayan Karimipour, Vahid |
| author_facet | Roofeh, Shayan Karimipour, Vahid |
| contents | In $d=2j+1$ dimensions, the Landau-Streater quantum channel is defined on the basis of spin $j$ representation of the $su(2)$ algebra. Only for $j=1$, this channel is equivalent to the Werner-Holevo channel and enjoys covariance properties with respect to the group $SU(3)$. We extend this class of channels to higher dimensions in a way which is based on the Lie algebra $so(d)$ and $su(d)$. As a result it retains its equivalence to the Werner-Holevo channel in arbitrary dimensions. The resulting channel is covariant with respect to the unitary group $SU(d)$. We then modify this channel in a way which can act as a noisy channel on qudits. The resulting modified channel now interpolates between the identity channel and the Werner-Holevo channel and its covariance is reduced to the subgroup of orthogonal matrices $SO(d)$. We then investigate some of the propeties of the resulting two-parameter family of channels, including their spectrum, their regions of lack of indivisibility, their Holevo quantity, entanglement-assisted capacity and the closed form of their complement channel and a possible lower bound for their quantum capacity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_11216 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Capacities of a two-parameter family of noisy Werner-Holevo channels Roofeh, Shayan Karimipour, Vahid Quantum Physics In $d=2j+1$ dimensions, the Landau-Streater quantum channel is defined on the basis of spin $j$ representation of the $su(2)$ algebra. Only for $j=1$, this channel is equivalent to the Werner-Holevo channel and enjoys covariance properties with respect to the group $SU(3)$. We extend this class of channels to higher dimensions in a way which is based on the Lie algebra $so(d)$ and $su(d)$. As a result it retains its equivalence to the Werner-Holevo channel in arbitrary dimensions. The resulting channel is covariant with respect to the unitary group $SU(d)$. We then modify this channel in a way which can act as a noisy channel on qudits. The resulting modified channel now interpolates between the identity channel and the Werner-Holevo channel and its covariance is reduced to the subgroup of orthogonal matrices $SO(d)$. We then investigate some of the propeties of the resulting two-parameter family of channels, including their spectrum, their regions of lack of indivisibility, their Holevo quantity, entanglement-assisted capacity and the closed form of their complement channel and a possible lower bound for their quantum capacity. |
| title | Capacities of a two-parameter family of noisy Werner-Holevo channels |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2405.11216 |