Pólya number of continuous-time quantum walks

Abstract

We propose a definition for the Pólya number of continuous-time quantum walks to characterize their recurrence properties. The definition involves a series of measurements on the system, each carried out on a different member from an ensemble in order to minimize the disturbance caused by it. We examine various graphs, including the ring, the line, higher dimensional integer lattices and a number of other graphs and calculate their Pólya number. For the timing of the measurements a Poisson process as well as regular timing are discussed. We find that the speed of decay for the probability at the origin is the key for recurrence.

arXiv comment8 pages, no figures. Accepted for publication in Physical Review A

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• Optimal Measurement Protocols in Quantum Zeno Effect
• Recurrence and Polya number of general one-dimensional random walks
• Shining Light on Quantum Transport in Fractal Networks
• Recurrence in discrete-time quantum stochastic walks
• On the Recurrence Character of the Hadamard walk in the Plane