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Title: Quantum Markov semigroups constructed from quantum Bernoulli noises

Quantum Bernoulli noises (QBNs) are the family of annihilation and creation operators acting on Bernoulli functionals, which can describe a two-level quantum system with infinitely many sites. In this paper, we consider the problem to construct quantum Markov semigroups (QMSs) directly from QBNs. We first establish several new theorems concerning QBNs. In particular, we define the number operator acting on Bernoulli functionals by using the canonical orthonormal basis, prove its self-adjoint property, and describe precisely its connections with QBN in a mathematically rigorous way. We then show the possibility to construct QMS directly from QBN. This is done by combining the general results on QMS with our new results on QBN obtained here. Finally, we examine some properties of QMS constructed from QBN.
Authors:
;  [1]
  1. School of Mathematics and Statistics, Northwest Normal University, Lanzhou, Gansu 730070 (China)
Publication Date:
OSTI Identifier:
22479636
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 57; Journal Issue: 2; Other Information: (c) 2016 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ANNIHILATION; CREATION OPERATORS; FUNCTIONALS; MARKOV PROCESS; NOISE; QUANTUM SYSTEMS