Quantum Markov semigroups constructed from quantum Bernoulli noises
- School of Mathematics and Statistics, Northwest Normal University, Lanzhou, Gansu 730070 (China)
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.
- OSTI ID:
- 22479636
- Journal Information:
- Journal of Mathematical Physics, Journal Name: Journal of Mathematical Physics Journal Issue: 2 Vol. 57; ISSN JMAPAQ; ISSN 0022-2488
- Country of Publication:
- United States
- Language:
- English
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