An analysis of the Aharonov-Anandan-Vaidman model

Pierre-Louis Giscard

Zhaoyan Wu, Jingxia Wang

Shan Gao

It is demonstrated that, based on an analysis of protective measurements, distinct quantum states cannot be compatible with a single state of reality. Recently Lewis et al (2012) 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 under-lying physical state. Their conclusion is based on an analysis of conventional projective measurements. Here we will demonstrate that protective measure-ments (Aharonov and Vaidman 1993; Aharonov, Anandan and Vaidman 1993), which are distinct from projective measurements, already shows that distinct quantum states cannot be compatible with a single state of reality. Projective measurements are one kind of measurements, for which the cou-pling 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 (when the system is not in one of the eigenstates of the mea-sured observable). This seems to leave space for ψ-epistemic models (Lewis et al 2012). 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 and

Shan Gao

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 cou-pling 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

D. Barseghyan, Pavel Exner

William George Unruh