Pauli channels exhibit a transition effect in memory estimation above a parametric threshold

Abstract

The classical communication capacities of quantum Pauli channels with memory are known to exhibit a transition effect. We revisit this phenomenon from the standpoint of the functionally analogous task of Pauli channel memory identification. We treat the complete class of Pauli channels with memory and determine the maximum quantum Fisher information achievable both with pure separable channel probe states and with maximally entangled bipartite probe states. A comparison of these Fisher informations reveals four distinct classes of Pauli channels and shows that only those channels that exceed a certain parametric threshold exhibit a transition effect. For those Pauli channels that exhibit this effect, the memory threshold at which it occurs has a simple analytic expression.