Grigori G. Amosov

On Weyl channels being covariant with respect to the maximum commutative group of unitaries

We investigate the Weyl channels being covariant with respect to the maximum commutative group of unitary operators. This class includes the quantum depolarizing channel and the “two-Pauli” channel as well. Then, we show that our estimation of the output entropy for a tensor product of the phase damping channel and the identity channel based upon the decreasing property of the relative entropy allows to prove the additivity conjecture for the minimal output entropy for the quantum depolarizing channel in any prime dimension and for the two-Pauli channel in the qubit case.

Remark on the additivity conjecture for a quantum depolarizing channel

We consider bistochastic quantum channels generated by unitary representations of a discrete group. We give a proof of the additivity conjecture for a quantum depolarizing channel Φ based on the decreasing property of the relative entropy. We show that the additivity conjecture holds for a channel Ξ = Ψ o Φ, where Ψ is a phase damping channel.

Strong superadditivity conjecture holds for the quantum depolarizing channel in any dimension

Given a quantum channel

A classical limit for the center-of-mass tomogram in view of the central limit theorem

\ensuremath{\Phi}

Transmitting qudits through larger quantum channels

in a Hilbert space

Quantum Probability Measures and Tomographic Probability Densities

H

Tomographic quantum measures for many degrees of freedom and the central limit theorem

, set

Towards a tomographic representation of quantum mechanics on the plane

{\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{H}}_{\ensuremath{\Phi}}(\ensuremath{\rho})={\mathrm{min}}_{{\ensuremath{\rho}}_{av}=\ensuremath{\rho}}{\ensuremath{\Sigma}}_{j=1}^{k}{\ensuremath{\pi}}_{j}S\mathbf{(}\ensuremath{\Phi}({\ensuremath{\rho}}_{j})\mathbf{)}

STATIONARY QUANTUM STOCHASTIC PROCESSES FROM THE COHOMOLOGICAL POINT OF VIEW

, where

Evolution equation of quantum tomograms for a driven oscillator in the case of the general linear quantization

{\ensuremath{\rho}}_{av}={\ensuremath{\Sigma}}_{j=1}^{k}{\ensuremath{\pi}}_{j}{\ensuremath{\rho}}_{j}