On the relationship between a quantum Markov semigroup and its representation via linear stochastic Schroedinger equations
arXiv:1405.6374 · doi:10.1007/s13226-015-0142-7
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.
16 pages
References in corpus (6)
- Existence, uniqueness and approximation of a stochastic Schrödinger equation: the diffusive case
- Entropic fluctuations of quantum dynamical semigroups
- Basic properties of nonlinear stochastic Schrödinger equations driven by Brownian motions
- Entropy Production for Quantum Markov Semigroups
- Quantum trajectories: memory and continuous observation
- Regularity of solutions to quantum master equations: A stochastic approach