Operational Concealment of Measurement Incompatibility by Quantum Channels

Abstract

Measurement incompatibility can remain intact at the operator level yet become operationally inaccessible when observations are restricted to the output of a quantum channel; we refer to this phenomenon as operational concealment. We develop a systematic adjoint-kernel framework for operational concealment in which observables are organized into operational equivalence classes determined by the kernel of the adjoint channel. This framework yields a structural classification of channels via kernel equivalence and monotonicity, together with a concealment robustness measure admitting explicit SDP formulations. It also yields an approximate concealment framework and a geometric characterization of concealment for unbiased binary qubit POVMs under rank-2 unital qubit channels. We show that concealment robustness coincides with standard incompatibility robustness for injective channels but can be strictly smaller for non-injective channels, as demonstrated by explicit analytical families. These results provide a systematic characterization and quantitative treatment of operationally inaccessible measurement incompatibility, with implications for restricted-access quantum information and semi-device-independent certification.