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

Abstract

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 dimesnsion and for the "two Pauli" channel in the qubit case.

A completely revised version, 20 pages

References in corpus (7)

• Coding Theorems for Quantum Channels
• Additivity for a class of unital qubit channels
• Additivity of the Classical Capacity of Entanglement-Breaking Quantum Channels
• On some additivity problems in quantum information theory
• On Weyl-covariant channels
• Maximal output purity and capacity for asymmetric unital qudit channels
• Additivity of minimal entropy output for a class of covariant channels

Cited by in corpus (16)

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• Quantum Stabilizer Codes Embedding Qubits Into Qudits
• Phase covariant qubit dynamics and divisibility
• Quantum channels irreducibly covariant with respect to the finite group generated by the Weyl operators
• The strong superadditivity conjecture holds for the quantum depolarizing channel in any dimension
• Classical capacity of the generalized Pauli channels
• On classical capacity of Weyl channels
• Some Open Problems in Quantum Information Theory
• On capacity of quantum channels generated by irreducible projective unitary representations of finite groups
• Quantum channels arising from abstract harmonic analysis
• On quantum channels and operations preserving finiteness of the von Neumann entropy
• On quantum tomography on locally compact groups
• Generalizations of $2$-dimensional diagonal quantum channels with constant Frobenius norm
• Phase-covariant mixtures of non-unital qubit maps
• On estimating the output entropy of a tensor product of the quantum phase-damping channel with an arbitrary channel
• On the additivity conjecture for the Weyl channels being covariant with respect to the maximum commutative group of unitaries