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

Mohamed Sabri, Etsuo Segawa, Martin Štefaňák

Research output: Contribution to journalArticle

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 prefactor 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 Pólya number. Our approach is based on path counting and the stationary phase approximation.

Original languageEnglish
Article number012136
JournalPhysical Review A
Volume98
Issue number1
DOIs
Publication statusPublished - 2018 Jul 27

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics

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