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 P <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">perp</sup> 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.