Maximal output purity and capacity for asymmetric unital qudit channels

Abstract

We consider generalizations of depolarizing channels to maps in which the identity channel is replaced by a convex combinations of unitary conjugations. We show that one can construct unital channels of this type for which the input which achieves maximal output purity is unique. We give conditions under which multiplicativity of the maximal p-norm and additivity of the minimal output entropy. We also show that the Holevo capacity need not equal log d - the minimal entropy as one might expect for a convex combination of unitary conjugations. Conversely, we give examples for which this condition holds, but the channel has no evident covariance properties.

Added a few references in v4. Previously added a section on numerical studies giving evidence for additivity of channel capacity, and comments on the relationship to quant-ph/0412133 and quant-ph/0505022

References in corpus (3)

• Classical information capacity of a class of quantum channels
• Extending additivity from symmetric to asymmetric channels
• Conditions for the multiplicativity of maximal l_p-norms of channels for fixed integer p

Cited by in corpus (17)

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• Pauli Diagonal Channels Constant on Axes
• Area-law entangled eigenstates from nullspaces of local Hamiltonians
• Nonadditivity effects in classical capacities of quantum multiple-access channels
• On Weyl channels being covariant with respect to the maximum commutative group of unitaries
• Extending additivity from symmetric to asymmetric channels
• The strong superadditivity conjecture holds for the quantum depolarizing channel in any dimension
• Simplification of additivity conjecture in quantum information theory
• Holevo Capacity of Discrete Weyl Channels
• Entanglement-Free Parameter Estimation of Generalized Pauli Channels
• Entangling and assisted entangling power of bipartite unitary operations
• Super-additivity in communication of classical information through quantum channels from a quantum parameter estimation perspective
• An algorithm to explore entanglement in small systems
• Capacities of Grassmann channels
• Transition of D- Level Quantum Systems Through Quantum Channels with Correlated Noise
• Exploring Non-Multiplicativity in the Geometric Measure of Entanglement
• New constructive counterexamples to additivity of minimum output Rényi p-entropy of quantum channels