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

Author

Listed:
  • Franco Fagnola

    (Politecnico di Milano)

  • Carlos Mora

    (Universidad de Concepción, Barrio Universitario)

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.

Suggested Citation

  • Franco Fagnola & Carlos Mora, 2015. "On the relationship between a quantum Markov semigroup and its representation via linear stochastic Schrödinger equations," Indian Journal of Pure and Applied Mathematics, Springer, vol. 46(4), pages 399-414, August.
    • Handle: RePEc:spr:indpam:v:46:y:2015:i:4:d:10.1007_s13226-015-0142-7
    DOI: 10.1007/s13226-015-0142-7
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