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Quantum simulations and quantum walks

Recurrence in monitored discrete time unitary dynamics

speaker: Reinhard F. Werner (Institut für Theoretische Physik, Leibniz Universität Hannover)

abstract: We consider a dynamical quantum process starting at a pure state \phi. In each step a fixed unitary operator U is applied followed by a projective measurement whether or not the particle is back at the initial state. The data are completely described by a measure on the unit circle, namely the \phi-expectation of spectral measure of U. We find that the process is recurrent (i.e., eventually returns with probability 1) if and only if the measure has no absolutely continuous part. In the recurrent case the expected return time is either infinite or an integer. This is paradoxical, since it implies that the return time, unlike all probabilities pertaining to experiments of finite duration, is a discontinuous function of the data. This is resolved by interpreting the expected return time as a winding number. (joint work with A Grünbaum, L. Velázques, A.H. Werner)

Wed 13 Nov, 15:00 - 16:00, Sala Stemmi
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