Measurement incompatibility is strictly stronger than disturbance

Marco Erba, Paolo Perinotti, Davide Rolino, Alessandro Tosini

Published 2023-05-26Version 1

The core of Heisenberg's argument for the uncertainty principle, involving the famous $\gamma$-ray microscope Gedankenexperiment, consists in the existence of measurements that irreversibly alter the state of the system on which they are acting, causing an irreducible disturbance on subsequent measurements. The argument was put forward to justify the existence of incompatible measurements, namely, measurements that cannot be performed jointly. In this Letter, on the one hand, we provide a compelling argument showing that incompatibility is indeed a sufficient condition for disturbance, while, on the other hand, we exhibit a toy theory that is a counterexample for the converse implication.