000127746 001__ 127746 000127746 005__ 20240319081011.0 000127746 0247_ $$2doi$$a10.1016/j.laa.2022.06.011 000127746 0248_ $$2sideral$$a129072 000127746 037__ $$aART-2022-129072 000127746 041__ $$aeng 000127746 100__ $$aLardizabal, C.F. 000127746 245__ $$aMean hitting time formula for positive maps 000127746 260__ $$c2022 000127746 5060_ $$aAccess copy available to the general public$$fUnrestricted 000127746 5203_ $$aIn 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. 000127746 536__ $$9info:eu-repo/grantAgreement/ES/DGA/E48-20R$$9info:eu-repo/grantAgreement/ES/MCIN/AEI/10.13039/501100011033 000127746 540__ $$9info:eu-repo/semantics/openAccess$$aby-nc-nd$$uhttp://creativecommons.org/licenses/by-nc-nd/3.0/es/ 000127746 590__ $$a1.1$$b2022 000127746 591__ $$aMATHEMATICS$$b101 / 329 = 0.307$$c2022$$dQ2$$eT1 000127746 591__ $$aMATHEMATICS, APPLIED$$b161 / 267 = 0.603$$c2022$$dQ3$$eT2 000127746 592__ $$a0.851$$b2022 000127746 593__ $$aAlgebra and Number Theory$$c2022$$dQ1 000127746 593__ $$aNumerical Analysis$$c2022$$dQ1 000127746 593__ $$aDiscrete Mathematics and Combinatorics$$c2022$$dQ1 000127746 593__ $$aGeometry and Topology$$c2022$$dQ2 000127746 594__ $$a2.2$$b2022 000127746 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/acceptedVersion 000127746 700__ $$0(orcid)0000-0002-3050-9540$$aVelázquez, L.$$uUniversidad de Zaragoza 000127746 7102_ $$12005$$2595$$aUniversidad de Zaragoza$$bDpto. Matemática Aplicada$$cÁrea Matemática Aplicada 000127746 773__ $$g650 (2022), 169-189$$pLinear algebra appl.$$tLINEAR ALGEBRA AND ITS APPLICATIONS$$x0024-3795 000127746 8564_ $$s367312$$uhttps://zaguan.unizar.es/record/127746/files/texto_completo.pdf$$yPostprint 000127746 8564_ $$s2297076$$uhttps://zaguan.unizar.es/record/127746/files/texto_completo.jpg?subformat=icon$$xicon$$yPostprint 000127746 909CO $$ooai:zaguan.unizar.es:127746$$particulos$$pdriver 000127746 951__ $$a2024-03-18-15:11:32 000127746 980__ $$aARTICLE