Abstract:
At the seminar we started talking about theories with hidden variables. Operational theories study statistical properties of processes of preparations and measurements over some systems – be they classical, quantum, or any other. To construct a hidden variable theory for a given theory is to try to describe that theory as a classical theory. This is done by mapping each preparation to some probability distribution over the phase space, and each measurement to some partition of unit over the phase space, and requiring that the statistics of the measurements be reproducible. We have discussed three simple hidden variable models for a two-level system and shown that each of them reproduces the measurement statistics, and each of them is taxed by some flaw – either sharp measurements are modeled by inaccurate measurements, or a pure state corresponds to a mixed probability distribution, or a single point in the phase space can correspond to several pure quantum states. In general, one can attempt to construct theories with hidden variables, but each such theory will have some drawbacks. For example, one cannot construct a theory in which pure states correspond to pure states and sharp measurements correspond to sharp measurements.
