Quantum channels irreducibly covariant with respect to the finite group generated by the Weyl operators
arXiv:1711.10823 · doi:10.1063/1.5013604
Abstract
We introduce a class of linear maps irreducibly covariant with respect to the finite group generated by the Weyl operators. This group provides a direct generalization of the quaternion group. In particular, we analyze the irreducibly covariant quantum channels; that is, the completely positive and trace-preserving linear maps. Interestingly, imposing additional symmetries leads to the so-called generalized Pauli channels, which were recently considered in the context of the non-Markovian quantum evolution. Finally, we provide examples of irreducibly covariant positive but not necessarily completely positive maps.
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- Classical capacity of the generalized Pauli channels
- Entanglement-Free Parameter Estimation of Generalized Pauli Channels
- Markovian semigroup from mixing non-invertible dynamical maps
- A covariant Stinespring theorem
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- Preservation of entanglement in local noisy channels