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Optical Fiber Communication Conference

Additivity for some product channels

Christopher King

Published Jan 1, 2001• 0 citations
Publisher

Abstract

We show that the Holevo bound, the minimal entropy, and the maximal p-norm are additive (respectively multiplicative) for some product quantum channels. The implications for information capacity of quantum channels are discussed.
DOI
10.1364/icqi.2001.pb31

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We show that for the tensor product of an entanglement-breaking quantum channel with an arbitrary quantum channel, both the minimum entropy of an output of the channel and the Holevo-Schumacher-Westmoreland capacity are additive. In addition, for the tensor product of two arbitrary quantum channels, we give a bound involving entanglement of formation for the amount of subadditivity (for minimum entropy output) or superadditivity (for classical capacity) that can occur. One of the more important open questions of quantum information theory is the determination of the capacity of a quantum channel for carrying classical information. This question has been only partially resolved. If entanglement between multiple inputs to the channel is not allowed, a formula for the classical capacity of a quantum channel has indeed been discovered [1, 2]. This capacity formula for a quantum channel Ψ is χ ∗ (Ψ) = max p i,ρ i H Ψ(piρi) − ∑