On Shor's channel extension and constrained channels

Details On Shor's channel extension and constrained channels On Shor's channel extension and constrained channels

2003-06-29

arxiv.org/abs/quant-ph/0306196v2

Commun. Math. Phys. v. 249,417-430, 2004

Physics

Quantum Physics

19 pages; substantially revised and enhanced. To appear in Commun. Math. Phys

Scientific paper

10.1007/s00220-004-1116-5

In this paper we give several equivalent formulations of the additivity conjecture for constrained channels, which formally is substantially stronger than the unconstrained additivity. To this end a characteristic property of the optimal ensemble for such a channel is derived, generalizing the maximal distance property. It is shown that the additivity conjecture for constrained channels holds true for certain nontrivial classes of channels. Recently P. Shor showed that conjectured additivity properties for several quantum information quantities are in fact equivalent. After giving an algebraic formulation for the Shor's channel extension, its main asymptotic property is proved. It is then used to show that additivity for two constrained channels can be reduced to the same problem for unconstrained channels, and hence, "global" additivity for channels with arbitrary constraints is equivalent to additivity without constraints.

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