Convex Trace Functions on Quantum Channels and the Additivity Conjecture

Details Convex Trace Functions on Quantum Channels and the Additivity Conjecture Convex Trace Functions on Quantum Channels and the Additivity Conjecture

2008-09-24

arxiv.org/abs/0809.4060v3

Phys. Rev. A 79, 052332 (2009)

Physics

Quantum Physics

9 pages, 1 figure. Published version

Scientific paper

10.1103/PhysRevA.79.052332

We study a natural generalization of the additivity problem in quantum information theory: given a pair of quantum channels, then what is the set of convex trace functions that attain their maximum on unentangled inputs, if they are applied to the corresponding output state? We prove several results on the structure of the set of those convex functions that are "additive" in this more general sense. In particular, we show that all operator convex functions are additive for the Werner-Holevo channel in 3x3 dimensions, which contains the well-known additivity results for this channel as special cases.

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