Reaching the Holevo Capacity via von Neumann measurement, and its use

Abstract

In this article we show that the Holevo capacity of a classical quantum channel, can be reached not only by a POVM but by von Neumann measurement too. Furthermore we show two use of this fact 1) We can generalize the classical compound channel to quantum environment and with this new measure technique we can give an optimal coding/decoding algorithm to it. 2) We give an algorithm, with it a classical system can be decoded by quantum apparatus in linear time, which is a surprising result, because best known optimal classical decoding algorithm need n*log(n) time. This means that if a quantum machine can perform arbitrarily von Neumann measurement with only two possible outcome, then it can solve non-polynomial classical problems in linear time.