Coherence-Sensitive Readout Models for Quantum Devices: Beyond the Classical Assignment Matrix

Readout error models for noisy quantum devices almost universally assume that measurement noise is classical: the measurement statistics are obtained from the ideal computational-basis populations by a column-stochastic assignment matrix A. This description is equivalent to assuming that the effective positive-operator-valued measurement (POVM) is diagonal in the measurement basis, and therefore completely insensitive to quantum coherences. We relax this assumption and derive a fully general expression for the observed measurement probabilities under arbitrary completely positive trace-preserving (CPTP) noise preceding a computational-basis measurement. Writing the ideal post-circuit stat ρ in terms of its populations x and coherences y, we show that the observed probability vector z satisfies z = A x + C y, where A is the familiar classical assignment matrix and C is a coherence-response matrix constructed from the off-diagonal matrix elements of the effective POVM in the computational basis. The classical model z = A x arises if and only if all POVM elements are diagonal; in this sense C quantifies accessible information about coherent readout distortions and interference between computational-basis states, all of which are invisible to models that retain only A. This work therefore provides a natural, fully general framework for coherence-sensitive readout modeling on current and future quantum devices.