Inverse quantum measurement problem
arXiv:1907.12480
The paper investigates when and how the complex phases of quantum probability amplitudes can be reconstructed from measured probability distributions and expectation values, effectively addressing the inverse problem of quantum measurement.
Abstract
Quantum mechanics relates probability of an observable event to the absolute square of the corresponding probability amplitude. It may, therefore, seem that the information about the amplitudes' phases must be irretrievably lost in the experimental data. Yet, there are experiments which report measurements of wave functions, and closely related quantities such as Bohm's velocities and positions of bohmian particles. We invert the question, and ask under which conditions the values of quantum amplitudes can be recovered from observed probability distributions and averages.
16 pages, 8 fucures