127746 20240319081011.0 doi 10.1016/j.laa.2022.06.011 sideral 129072 ART-2022-129072 eng Lardizabal, C.F. Mean hitting time formula for positive maps 2022 Access copy available to the general public Unrestricted In the classical theory of Markov chains, one may study the mean time to reach some chosen state, and it is well-known that in the irreducible, finite case, such quantity can be calculated in terms of the fundamental matrix of the walk, as stated by the mean hitting time formula. In this work, we present an analogous construction for the setting of irreducible, positive, trace preserving maps. The reasoning on positive maps generalizes recent results given for quantum Markov chains, a class of completely positive maps acting on graphs, presented by S.Gudder. The tools employed in this work are based on a proper choice of block matrices of operators, inspired in part by recent work on Schur functions for closed operators on Banach spaces, due to F.A.Grünbaum and one of the authors. The problem at hand is motivated by questions on quantum information theory, most particularly the study of quantum walks, and provides a basic context on which statistical aspects of quantum evolutions on finite graphs can be expressed in terms of the fundamental matrix, which turns out to be an useful generalized inverse associated with the dynamics. As a consequence of the wide generality of the mean hitting time formula found in this paper, we have obtained extensions of the classical version, either by assuming only the knowledge of the probabilistic distribution for the initial state, or by enlarging the arrival state to a subset of states. info:eu-repo/grantAgreement/ES/DGA/E48-20R info:eu-repo/grantAgreement/ES/MCIN/AEI/10.13039/501100011033 info:eu-repo/semantics/openAccess by-nc-nd http://creativecommons.org/licenses/by-nc-nd/3.0/es/ 1.1 2022 MATHEMATICS 101 / 329 = 0.307 2022 Q2 T1 MATHEMATICS, APPLIED 161 / 267 = 0.603 2022 Q3 T2 0.851 2022 Algebra and Number Theory 2022 Q1 Numerical Analysis 2022 Q1 Discrete Mathematics and Combinatorics 2022 Q1 Geometry and Topology 2022 Q2 2.2 2022 info:eu-repo/semantics/article info:eu-repo/semantics/acceptedVersion Velázquez, L. Universidad de Zaragoza (orcid)0000-0002-3050-9540 2005 595 Universidad de Zaragoza Dpto. Matemática Aplicada Área Matemática Aplicada 650 (2022), 169-189 Linear algebra appl. LINEAR ALGEBRA AND ITS APPLICATIONS 0024-3795 367312 http://zaguan.unizar.es/record/127746/files/texto_completo.pdf Postprint 2297076 http://zaguan.unizar.es/record/127746/files/texto_completo.jpg?subformat=icon icon Postprint oai:zaguan.unizar.es:127746 articulos driver 2024-03-18-15:11:32 ARTICLE