Site recurrence of open and unitary quantum walks on the line

Site recurrence of open and unitary quantum walks on the line We study the problem of site recurrence of discrete-time nearest-neighbor open quantum random walks (OQWs) on the integer line, proving basic properties and some of its relations with the corresponding problem for unitary (coined) quantum walks (UQWs). For both kinds of walks, our discussion concerns two notions of recurrence, one given by a monitoring procedure (Grünbaum et al. in Commun Math Phys 320:543–569, 2013; Lardizabal and Souza in J Stat Phys 159:772–796, 2015), and we study their similarities and differences. In particular, by considering UQWs and OQWs induced by the same pair of matrices, we discuss the fact that recurrence of these walks is related by an additive interference term in a simple way. Based on a previous result of positive recurrence, we describe an open quantum version of Kac’s lemma for the expected return time to a site. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quantum Information Processing Springer Journals

Site recurrence of open and unitary quantum walks on the line

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Publisher
Springer US
Copyright
Copyright © 2016 by Springer Science+Business Media New York
Subject
Physics; Quantum Information Technology, Spintronics; Quantum Computing; Data Structures, Cryptology and Information Theory; Quantum Physics; Mathematical Physics
ISSN
1570-0755
eISSN
1573-1332
D.O.I.
10.1007/s11128-016-1483-9
Publisher site
See Article on Publisher Site

Abstract

We study the problem of site recurrence of discrete-time nearest-neighbor open quantum random walks (OQWs) on the integer line, proving basic properties and some of its relations with the corresponding problem for unitary (coined) quantum walks (UQWs). For both kinds of walks, our discussion concerns two notions of recurrence, one given by a monitoring procedure (Grünbaum et al. in Commun Math Phys 320:543–569, 2013; Lardizabal and Souza in J Stat Phys 159:772–796, 2015), and we study their similarities and differences. In particular, by considering UQWs and OQWs induced by the same pair of matrices, we discuss the fact that recurrence of these walks is related by an additive interference term in a simple way. Based on a previous result of positive recurrence, we describe an open quantum version of Kac’s lemma for the expected return time to a site.

Journal

Quantum Information ProcessingSpringer Journals

Published: Dec 17, 2016

References

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