On the relationship between a quantum Markov semigroup and its representation via linear stochastic Schrödinger equations

Franco Fagnola () and Carlos Mora ()
Additional contact information
Franco Fagnola: Politecnico di Milano
Carlos Mora: Universidad de Concepción, Barrio Universitario

Indian Journal of Pure and Applied Mathematics, 2015, vol. 46, issue 4, 399-414

Abstract: 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, stronger than irreducibility of the quantum Markov semigroup, nevertheless, they are equivalent for some important classes of semigroups.

Keywords: Open quantum systems; quantum Markov semigroups; stochastic Schrödinger equations; irreducibility; support of quantum states; control (search for similar items in EconPapers)
Date: 2015
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s13226-015-0142-7 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:indpam:v:46:y:2015:i:4:d:10.1007_s13226-015-0142-7

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/13226

DOI: 10.1007/s13226-015-0142-7

Access Statistics for this article

Indian Journal of Pure and Applied Mathematics is currently edited by Nidhi Chandhoke

More articles in Indian Journal of Pure and Applied Mathematics from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().