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A sufficient condition on concavity of the auxiliary function appearing in quantum reliability function

Shigeru Furuichi, Kenjiro Yanagi, Ken Kuriyama

Published Jan 1, 2003• 4 citations
OpenAlex

Abstract

A suMcient condition on concavity of the auxiliary function which appears in the random coding exponent as the lower bound of the qu'antum reliability function for general quantum states is noted.The validity of its suMcient condition is shown by some numerical computatlons.

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•Jan 1, 2006•0 citations
The auxiliary function of a classical channel appears in two fundamental quantities, the random coding exponent and the sphere-packing exponent, which yield upper and lower bounds on the error probability of decoding, respectively. A crucial property of the auxiliary function is its concavity, and this property consequently leads to several important results in finite blocklength analysis. In this paper, we prove that the auxiliary function of a classical-quantum channel also enjoys the same concavity property, extending an earlier partial result to its full generality. We also prove that the auxiliary function satisfies the data-processing inequality, among various other important properties. Furthermore, we show that the concavity property of the auxiliary function enables a geometric interpretation of the random coding exponent and the sphere-packing exponent of a classical-quantum channel. The key component in our proof is an important result from the theory of matrix geometric means.