Simplification of additivity conjecture in quantum information theory

Abstract

We simplify some conjectures in quantum information theory; the additivity of minimal output entropy, the multiplicativity of maximal output p-norm and the superadditivity of convex closure of output entropy. We construct a unital channel for a given channel so that they share the above additivity properties; we can reduce the conjectures for all channels to those for unital channels.

8 pages

References in corpus (8)

• Remarks on the classical capacity of quantum channel
• Strong superadditivity of the entanglement of formation follows from its additivity
• Additivity of minimal entropy output for a class of covariant channels
• A quantum channel with additive minimum output entropy
• An application of a matrix inequality in quantum information theory
• Note on multiple additivity of minimal Renyi entropy output of the Werner-Holevo channels
• Additivity for transpose depolarizing channels
• Remark on the additivity conjecture for the quantum depolarizing channel

Cited by in corpus (5)

• Simplifying additivity problems using direct sum constructions
• Additivity and Distinguishability of Random Unitary Channels
• Some Open Problems in Quantum Information Theory
• The classical capacity of quantum channels with memory
• Computational Distinguishability of Quantum Channels