Abstract:
Recurrence of a random walk is characterized by the so-called Pólya
number which denotes the probability that the particle returns to the
origin at least once during the whole time evolution. We extend the
concept of recurrence from classical random walks to quantum walks.
First, we show that recurrence of a quantum walk is influenced by the
additional degrees of freedom offered by quantum mechanics. Second,
we discuss the effect of bias on the recurrence properties of a
quantum walk. Finally, we illustrate on a simple example that
stationary solutions and full revivals are possible in quantum walks.
