Conditional limit measure of one-dimensional quantum walk with absorbing sink

Abstract

We consider a two-state quantum walk on a line where after the first step an absorbing sink is placed at the origin. The probability of finding the walker at position $j$, conditioned on that it has not returned to the origin, is investigated in the asymptotic limit. We prove a limit theorem for the conditional probability distribution and show that it is given by the Konno's density function modified by a pre-factor ensuring that the distribution vanishes at the origin. In addition, we discuss the relation to the problem of recurrence of a quantum walk and determine the Polya number. Our approach is based on path counting and stationary phase approximation.

arXiv comment9 pages, 6 figures; added journal reference, updated to the published version

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Cited by in corpus (2)

• Monitored Recurrence of a One-parameter Family of Three-state Quantum Walks
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