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Mathematics > Probability

arXiv:1405.6374 (math)
[Submitted on 25 May 2014 (v1), last revised 2 Oct 2014 (this version, v2)]

Title:On the relationship between a quantum Markov semigroup and its representation via linear stochastic Schroedinger equations

Authors:Franco Fagnola, Carlos Mora
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Abstract:A quantum Markov semigroup can be represented via classical diffusion processes solving a stochastic Schrödinger equation. In this paper we first prove that a quantum Markov semigroup is irreducible if and only if classical diffusion processes are total in the Hilbert space of the system. Then we study the relationship between irreducibility of a quantum Markov semigroup and properties of these diffusions such as accessibility, the Lie algebra rank condition, and irreducibility. We prove that all these properties are, in general, weaker than irreducibility of the quantum Markov semigroup, nevertheless, they are equivalent for some important classes of semigroups.
Comments: 16 pages
Subjects: Probability (math.PR)
MSC classes: 60H15, 46L55, 60H30, 81S22
Cite as: arXiv:1405.6374 [math.PR]
  (or arXiv:1405.6374v2 [math.PR] for this version)
  https://doi.org/10.48550/arXiv.1405.6374
Journal reference: Indian J. Pure Appl. Math., 46(4): 399-414, August 2015
Related DOI: https://doi.org/10.1007/s13226-015-0142-7

Submission history

From: Franco Fagnola [view email]
[v1] Sun, 25 May 2014 10:45:05 UTC (14 KB)
[v2] Thu, 2 Oct 2014 14:33:58 UTC (14 KB)
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