QuantumChannels / CONCEPT

Three-weight Pauli channels have Bayesian inverses only at the maximally mixed state

Ting, Fullwood and Wu (arXiv:2605.10375) characterize when a unital qubit channel has a Bayesian inverse with respect to a state, and for Pauli channels with exactly three non-zero weights leave open whether the maximally mixed state is the only such state. It is: for every Pauli channel whose probability vector has exactly three non-zero entries, a completely positive trace-preserving Bayesian inverse with respect to a qubit state exists if and only if the state is the maximally mixed state.