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Research papers

Quantum Polya theorem

A. N. Bondarenko, V. A. Dedok

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences

Abstract: In this paper we discuss return probability properties of quantum random walk on the line. In the classical case this property is well known as the Polya theorem. We study in detail not only usually discussed “Hadamar walk”. In the general case quantum random walk depends on parameter $\theta$ ($0\le\theta\le\pi$). It was shown that in the most of cases when $0<\theta<\pi$ quantum random walk is weak localized and recurrent and the return probability tends to $0$ with the speed $1/t$. Other cases are also studied and described.

Keywords: quantum random walk, return probability, Polya theorem.

UDC: 519.214

MSC: 60F99

Received March 16, 2009, published September 10, 2009

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