Capacities of a two-parameter family of noisy Werner-Holevo channels

• URL: http://arxiv.org/abs/2405.11216v2
• Date: Sat, 8 Jun 2024 13:54:36 GMT
• Title: Capacities of a two-parameter family of noisy Werner-Holevo channels
• Authors: Shayan Roofeh, Vahid Karimipour,
• Abstract summary: In $d=2j+1$ dimensions, the Landau-Streater quantum channel is defined on the basis of spin $j$ representation of the $su(2)$ algebra. We extend this class of channels to higher dimensions in a way which is based on the Lie algebra $so(d)$ and $su(d)$.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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