Title: Quantum Probability Tutorial II
Speaker: Roman Belavkin (Middlesex University)

Abstract:
In the second part of the tutorial we shall discuss quantum version of the law of total probability, and define the notion of causal predictability (or compatibility) of observables.  We shall discuss the problem of observing and predicting a motion of a free quantum particle, and discuss some paradoxes arising in this problem.  The solution using non-demolition (or indirect) measurement will be briefly discussed, and the uncertainty relation between the error of measurement and the Langevin force perturbing the particle due to measurement will be introduced.  Using the quantum causality principle we shall demonstrate that non-trivial interaction between a quantum and classical systems is time irreversible, and that such a time-asymmetric dynamics can be realized by a unitary operator only if it acts on an infinite-dimensional Hilbert space.