2016/07/31 by Silas L. Carvalho, Leonardo F. Guidi, Carlos F. Lardizabal · 16 citations
Computer Science · Mathematics · Physics and Astronomy · #Complexity and Algorithms in Graphs #Integer (computer science) #Quantum #Quantum Computing Algorithms and Architecture #Quantum computer #Quantum walk #Quantum-Dot Cellular Automata #Random walk #Real line #Simple (philosophy) #Unitary state #math-ph #math.MP #math.PR #quant-ph
paper · pdf · doi:10.1007/s11128-016-1483-9
published in Quantum Information Processing 16(1) (Springer Science+Business Media)
openalex created_date 2016/08/23 · arxiv created 2016/09/29 · openalex publication_date 2016/12/17 · arxiv updated 2017/11/13 · openalex updated_date 2026/08/05
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, another in terms of Pólya numbers, 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 are 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.