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We study the problem of site recurrence of discrete time nearest neighboropen quantum random walks (OQWs) on the integer line, proving basic propertiesand some of its relations with the corresponding problem for unitary (coined)quantum walks (UQWs). For both kinds of walks our discussion concerns twonotions of recurrence, one given by a monitoring procedure, another in terms ofP\'olya numbers, and we study their similarities and differences. Inparticular, 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 additiveinterference term in a simple way. Based on a previous result of positiverecurrence we describe an open quantum version of Kac's lemma for the expectedreturn time to a site.

Site recurrence of open and unitary quantum walks on the line