Comment on “Distinct Quantum States Can Be Compatible with a Single State of Reality”

In their Letter [1], Lewis et al. demonstrated that additional assumptions such as preparation independence are always necessary to rule out a ψ-epistemic model, in which the quantum state is not uniquely determined by the underlying physical state. Here we point out that these authors ignored the important work of Aharonov, Anandan and Vaidman on protective measurements [2-5], and their conclusion, which is based only on an analysis of conventional projective measurements, is not true. Projective measurements are one kind of measurements, for which the coupling between the measuring device and the measured system is very strong and almost instantaneous, and the measurement results are the eigenvalues of the measured observable. Due to the resulting collapse of the wave function, such impulsive measurements cannot measure the actual physical state of the measured system. This seems to leave space for ψ-epistemic models [1]. Thanks to the work of Aharonov et al, however, it has been known that the coupling strength and the measuring time can be adjusted for a standard measurement procedure, and there also exist other kinds of measurements such as weak measurements [6] and protective measurements [2-5] (Note that weak measurements have been implemented in experiments [7], and it can be reasonably expected that protective measurements can also be implemented in the near future with the rapid development of quantum technologies). In particular, the actual physical state of the measured system can be measured by a series of protective measurements, and the wave function turns out to be a one-to-one representation of the physical state [2-5]. Therefore, the ψ-epistemic models, in which the wave function or quantum state is not uniquely determined by the underlying physical state, can be ruled out without resorting to nontrivial assumptions beyond those required for a well-formed ontological model. A general method of protective measurements is to let the measured system be in a nondegenerate eigenstate of the whole Hamiltonian using a suitable protective interaction, and then make the measurement adiabatically so that the state of the system neither collapses nor becomes entangled with the measuring device appreciably. In this way, such protective measurements can measure the expectation values of observables on a single quantum system [2-5]. As a simple example, consider a quantum system in a discrete nondegenerate energy eigenstate ψ(x). In this case, the system itself supplies the protection of the state due to energy conservation and no artificial protection is needed. We take