An Extreme form of Superactivation for Quantum Zero-Error Capacities

TL;DR

This paper demonstrates an extreme form of superactivation in quantum channels where two channels with zero zero-error classical capacity can combine to have a positive zero-error quantum capacity, revealing a novel non-additivity property.

Contribution

It proves the existence of quantum channels exhibiting simultaneous superactivation of classical and quantum zero-error capacities, a phenomenon not observed in classical channels.

Findings

Existence of channels with zero classical capacity but positive quantum capacity when combined

Superactivation can occur simultaneously for classical and quantum zero-error capacities

This phenomenon is a stronger form of superactivation not previously known in quantum information theory

Abstract

The zero-error capacity of a channel is the rate at which it can send information perfectly, with zero probability of error, and has long been studied in classical information theory. We show that the zero-error capacity of quantum channels exhibits an extreme form of non-additivity, one which is not possible for classical channels, or even for the usual capacities of quantum channels. By combining probabilistic arguments with algebraic geometry, we prove that there exist channels E1 and E2 with no zero-error classical capacity whatsoever, C_0(E1) = C_0(E2) = 0, but whose joint zero-error quantum capacity is positive, Q_0(E1 x E2) >= 1. This striking effect is an extreme from of the superactivation phenomenon, as it implies that both the classical and quantum zero-error capacities of these channels can be superactivated simultaneously, whilst being a strictly stronger property of capacities. Superactivation of the quantum zero-error capacity was not previously known.