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Symbols of mixed unitary quantum channels generated by finite unitary groups

Grigori Gennadievich Amosov, Danil D. Cheremukhin

WORLD SCIENTIFIC eBooksAug 1, 20250 citations

Classical capacity of Weyl channel invariant with respect to the action of a unitary representation of the cyclic group

Grigori Gennadievich Amosov

Jun 10, 20200 citations

The Role of Covariancy in Calculating Capacity of Quantum Channels Generated by Projective Unitary Representations of Non-Abelian Groups

Grigori Gennadievich Amosov, L. A. Ryskin

Abstract We study quantum channels generated by irreducible projective unitary representations of finite groups. It is shown that to calculate a classical capacity of channel it is not necessary to claim that it is covariant with respect to a representation. It helps to consider non-Abelian groups because in this case such channels are not covariant respect to the generating representation.

Lobachevskii Journal of MathematicsJun 1, 20241 citation

ON CAPACITIES OF QUANTUM CHANNELS

Masanori Ohya, Dėnes Petz, Noboru Watanabe

WORLD SCIENTIFIC eBooksFeb 1, 200836 citations

Structure of irreducibly covariant quantum channels for finite groups

Marek Mozrzymas, Michał Studziński, Nilanjana Datta

We obtain an explicit characterization of linear maps, in particular, quantum channels, which are covariant with respect to an irreducible representation (U) of a finite group (G), whenever U⊗Uc is simply reducible (with Uc being the contragradient representation). Using the theory of group representations, we obtain the spectral decomposition of any such linear map. The eigenvalues and orthogonal projections arising in this decomposition are expressed entirely in terms of representation characteristics of the group G. This in turn yields necessary and sufficient conditions on the eigenvalues of any such linear map for it to be a quantum channel. We also obtain a wide class of quantum channels which are irreducibly covariant by construction. For two-dimensional irrreducible representations of the symmetric group S(3), and the quaternion group Q, we also characterize quantum channels which are both irreducibly covariant and entanglement breaking.We obtain an explicit characterization of linear maps, in particular, quantum channels, which are covariant with respect to an irreducible representation (U) of a finite group (G), whenever U⊗Uc is simply reducible (with Uc being the contragradient representation). Using the theory of group representations, we obtain the spectral decomposition of any such linear map. The eigenvalues and orthogonal projections arising in this decomposition are expressed entirely in terms of representation characteristics of the group G. This in turn yields necessary and sufficient conditions on the eigenvalues of any such linear map for it to be a quantum channel. We also obtain a wide class of quantum channels which are irreducibly covariant by construction. For two-dimensional irrreducible representations of the symmetric group S(3), and the quaternion group Q, we also characterize quantum channels which are both irreducibly covariant and entanglement breaking.

arXiv:1610.05657Journal of Mathematical PhysicsMay 1, 201731 citations

Finite groups and quantum theory

D. B. Chesnut

Jan 1, 197413 citations

On capacity of quantum channels generated by irreducible projective unitary representations of finite groups

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