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dc.contributor.authorVourdas, Apostolos
dc.date.accessioned2022-03-18T10:39:14Z
dc.date.accessioned2022-03-23T14:26:34Z
dc.date.available2022-03-18T10:39:14Z
dc.date.available2022-03-23T14:26:34Z
dc.date.issued2022-05
dc.identifier.citationVourdas A (2022) Markov chains with doubly stochastic transition matrices and application to a sequence of non-selective quantum measurements. Physica A: Statistical Mechanics and its Applications. 593: 126911en_US
dc.identifier.urihttp://hdl.handle.net/10454/18802
dc.identifier.urihttp://hdl.handle.net/10454/18802
dc.descriptionyesen_US
dc.description.abstractA time-dependent finite-state Markov chain that uses doubly stochastic transition matrices, is considered. Entropic quantities that describe the randomness of the probability vectors, and also the randomness of the discrete paths, are studied. Universal convex polytopes are introduced which contain all future probability vectors, and which are based on the Birkhoff–von Neumann expansion for doubly stochastic matrices. They are universal in the sense that they depend only on the present probability vector, and are independent of the doubly stochastic transition matrices that describe time evolution in the future. It is shown that as the discrete time increases these convex polytopes shrink, and the minimum entropy of the probability vectors in them increases. These ideas are applied to a sequence of non-selective measurements (with different projectors in each step) on a quantum system with -dimensional Hilbert space. The unitary time evolution in the intervals between the measurements, is taken into account. The non-selective measurements destroy stroboscopically the non-diagonal elements in the density matrix. This ‘hermaphrodite’ system is an interesting combination of a classical probabilistic system (immediately after the measurements) and a quantum system (in the intervals between the measurements). Various examples are discussed. In the ergodic example, the system follows asymptotically all discrete paths with the same probability. In the example of rapidly repeated non-selective measurements, we get the well known quantum Zeno effect with ‘frozen discrete paths’ (presented here as a biproduct of our general methodology based on Markov chains with doubly stochastic transition matrices).en_US
dc.language.isoenen_US
dc.rights© 2022 Elsevier. Reproduced in accordance with the publisher's self-archiving policy. This manuscript version is made available under the CC-BY-NC-ND 4.0 license.en
dc.subjectMarkov chains with doubly stochastic transition matricesen_US
dc.subjectNon-selective quantum measurementsen_US
dc.titleMarkov chains with doubly stochastic transition matrices and application to a sequence of non-selective quantum measurementsen_US
dc.status.refereedyesen_US
dc.date.application2022-01-20
dc.typeArticleen_US
dc.type.versionAccepted manuscripten_US
dc.identifier.doihttps://doi.org/10.1016/j.physa.2022.126911
dc.rights.licenseUnspecifieden_US
dc.date.updated2022-03-18T10:39:16Z
refterms.dateFOA2022-03-23T14:27:31Z
dc.openaccess.statusEmbargoed accessen_US
dc.date.accepted2021-10-14


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