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arXiv · 1807.02765

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

Mohamed Sabri·Etsuo Segawa·Martin Stefanak
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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.

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Mohamed Sabri, Etsuo Segawa, Martin Stefanak. 2018-08-07. Conditional limit measure of one-dimensional quantum walk with absorbing sink. https://doi.org/10.1103/physreva.98.012136

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