Information geometric superactivation of classical zero-error capacity of quantum channels

Abstract

This paper introduces a fundamentally new method of finding the conditions for the superactivation of the zero-error capacity of quantum channels. The zero-error capacity of the quantum channel describes the amount of information which can be transmitted perfectly through a noisy quantum channel. The superactivation of the zero-error capacity of quantum channels makes it possible to use two quantum channels, each with zero zero-error capacity, with a positive joint zero-error capacity. Currently we have no theoretical background for describing all possible combinations of superactive quantum channels, hence there should be many other possible combinations. We give an algorithmic solution to the problem. To analyze the superactivation of the zero-error capacity, we introduce a new geometrical representation, called the quantum superball. Our method can be the first efficient algorithmic solution to discover the still unknown combinations to determine the superactivation of the zero-error capacity of quantum channels, without the extremely high computational costs.