Distinct Quantum States Cannot Be Compatible with a Single State of Reality

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 underlying physical state. Their conclusion is based on an analysis of conventional projective measurements. Here we will demonstrate that protective measurements (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 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 (when the system is not in one of the eigenstates of the measured 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 protective measurements (Aharonov, Albert and Vaidman 1988; Aharonov and Vaidman 1993; Aharonov, Anandan and Vaidman 1993). Protective measurement uses a weak and long duration coupling interaction and an appropriate procedure to protect the measured system from being disturbed. A general scheme is to let the measured system be in a nondegenerate eigenstate of the whole Hamiltonian using a suitable protective interaction (in some situations the protection is provided by the measured system itself), 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 ∗Institute for the History of Natural Sciences, Chinese Academy of Sciences, Beijing 100190, P. R. China. E-mail: [email protected]. 1Note that weak measurements have been implemented in experiments (Lundeen et al 2011), and it can be reasonably expected that protective measurements can also be implemented in the near future with the rapid development of quantum technologies.