Extending additivity from symmetric to asymmetric channels

Abstract

We prove a lemma which allows one to extend results about the additivity of the minimal output entropy from highly symmetric channels to a much larger class. A similar result holds for the maximal output $p$-norm. Examples are given showing its use in a variety of situations. In particular, we prove the additivity and the multiplicativity for the shifted depolarising channel.

8 pages. This is the latest version of the first half of the original paper. The other half will appear in another paper

References in corpus (3)

• Classical information capacity of a class of quantum channels
• Maximal output purity and capacity for asymmetric unital qudit channels
• Conditions for the multiplicativity of maximal l_p-norms of channels for fixed integer p

Cited by in corpus (15)

• Strong converse for the classical capacity of entanglement-breaking and Hadamard channels via a sandwiched Renyi relative entropy
• Counterexamples to the maximal p-norm multiplicativity conjecture for all p > 1
• Trade-off capacities of the quantum Hadamard channels
• Semidefinite programming strong converse bounds for classical capacity
• Pauli Diagonal Channels Constant on Axes
• Maximal output purity and capacity for asymmetric unital qudit channels
• Simplification of additivity conjecture in quantum information theory
• Qubit channels with small correlations
• Capacities of Grassmann channels
• Capacities of the covariant Pauli channel
• Additivity rates and PPT property for random quantum channels
• New multiplicativity results for qubit maps
• Additive bounds of minimum output entropies for unital channels and an exact qubit formula
• An application of decomposable maps in proving multiplicativity of low dimensional maps
• Convex Trace Functions on Quantum Channels and the Additivity Conjecture