A general formulation of the modulation function approach to von Neumann - Wigner type potentials is given covering recent discussions of such potentials as special cases.
We derive a direct reconstruction algorithm for the discrete Wigner function through different types of measurements. For a system described in a Hilbert space of dimension N=N1…Np, where the numbers Ni are prime, the reconstruction is accomplished with (N1+1)…(Np+1) factorable (local) von Neumann measurements. For the special case where the dimension is a power of a prime, the reconstruction can be performed in a much more efficient way using N+1 complementary measurements. If the system is composed of a number of smaller subsystems, these measurements will then in general be nonseparable.
Abstract This chapter begins by discussing the foundations of Hugh Everett III's relative state theory, which he regards as a new, more general, and complete theory than the standard von Neumann–Dirac theory. It then talks about why Albert Einstein rejected Max Born's formulation of quantum mechanics where he described his new statistical interpretation of the wave function. It also provides a discussion on von Neumann's formulation of quantum mechanics and the standard theory, as well as a summary of the said theory. The chapter goes on to detail several arguments presented by Einstein regarding von Neumann's interpretation of quantum mechanics. It then presents von Neumann's psychophysical parallelism and Wigner's friend experiment.