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We characterize the completely positive trace-preserving maps on qutrits (qutrit channels) according to their covariance and symmetry properties. Both discrete and continuous groups are considered. It is shown how each symmetry group restricts arbitrariness in the parameters of the channel to a very small set. Although the explicit examples are related to qutrit channels, the formalism is sufficiently general to be applied to qudit channels  

In this paper, we investigate reliable transmission of three correlated discrete memoryless sources over a two-relay network. In our considered model, one of the sources is available at the sender whereas, the other two sources are known to the first and the second relay. We present both joint and separate source-channel coding schemes, and derive the corresponding sets of sufficient conditions for reliable sources transmission. The manner of cooperation in both schemes is Decode-and-Forward strategy. In the joint approach, we generalize the correlation preserving mapping technique to our model using nested backward decoding. Our proposed separate approach is based on Slepian-Wolf source... 

In general quantum operations, or quantum channels cannot be inverted by physical operations, i.e., by completely positive trace-preserving maps. An arbitrary state passing through a quantum channel loses its fidelity with the input. Given a quantum channel E, we discuss the concept of its quasi-inverse as a completely positive trace-preserving map Eqi which when composed with E increases its average input-output fidelity in an optimal way. The channel Eqi comes as close as possible to the inverse of a quantum channel. We give a complete classification of such maps for qubit channels and provide quite a few illustrative examples. © 2020 American Physical Society  

Constructing all extreme instances of the set of completely positive trace-preserving (CPTP) maps, i.e., quantum channels, is a challenging and valuable open problem in quantum information theory. Here we introduce a systematic approach that, despite the lack of knowledge about the full parametrization of the set of CPTP maps on arbitrary Hilbert-spaced dimension, enables us to construct exactly those extreme channels that are covariant with respect to a finite discrete group or a compact connected Lie group. Innovative labeling of quantum channels by group representations enables us to identify the subset of group-covariant channels whose elements are group-covariant generalized-extreme...