Quantum Disturbance without State Change: Soundness and Locality of Disturbance Measures

Abstract: It is often supposed that a quantum system is not disturbed without state change. In a recent debate, this assumption is used to claim that the operator-based disturbance measure, a broadly used disturbance measure, has an unphysical property. Here, we show that a quantum system possibly incurs an operationally detectable disturbance without state change to rebut the claim. Moreover, we establish the reliability, formulated as soundness and locality, of the operator-based disturbance measure, which, we show, quantifies the disturbance on an observable that manifests in the time-like correlation even in the case where its probability distribution does not change.