The classical communication capacities of quantum Pauli channels with memory (correlation) are known to exhibit a transition effect. We revisit this phenomenon from the standpoint of the functionally analogous task of Pauli channel correlation identification. We treat the complete class of Pauli channels with correlation 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 threshold at which it occurs has a simple analytic expression.
Quantum Fisher Information of a Teleported State in Heisenberg XYZ Chain with Magnetic Field and Kaplan–Shekhtman–Entin-Wohlman–Aharony Interaction
