On Uffink’s alternative interpretation of protective measurements

Protective measurement is a new measuring method introduced by Aharonov, Anandan and Vaidman (1993). By a protective measurement, one can measure the expectation value of an observable on a single quantum system, even if the system is initially not in an eigenstate of the measured observable. Aharonov, Anandan and Vaidman attributed this feature of protective measurements to a physical manifestation of the wave function of the system. This interpretation was challenged by Uffink (1999, 2012). He argued that only observables that commute with the system’s Hamiltonian can be protectively measured, and a protective measurement of an observable that does not commute with the system’s Hamiltonian does not actually measure the observable, but measure another related observable that commutes with the system’s Hamiltonian. In this paper, we argue that there are several errors in Uffink’s arguments, and his alternative interpretation of protective measurements is untenable.