Zero-error capacity of quantum channels and noiseless subsystems

Abstract

This paper investigates connections between the theory of quantum noiseless subsystems and the zero-error capacity of quantum channels. In particular, we show that if we have a noiseless subsystem state p supported by a projector P, then any quantum state with components in the subspace Pperp is adjacent to p. This result has some interesting implications for the quantum states of the optimum (S,V) for which the zero-error capacity is reached.