Structure of uniformly continuous quantum Markov semigroups (Q2800851)

The authors provide the structural characterization of the generator of uniformly continuous quantum Markov semigroups which admit a decoherence-free subalgebra, on which the semigroup acts as a semigroup of automorphisms. The characterization applies for the case of an atomic subalgebra, given by a type-I factor or a direct sum of type-I factors. It is shown that in this scenario the decoherence-free part of the system evolves independently from the part affected by environmental noise. The system Hilbert space can then be seen as the tensor product of two Hilbert spaces, and the Lindblad operators appearing in the Gorini-Kossakowski-Sudarshan-Lindblad representation of the generator act only on one of the two Hilbert spaces. The proven results allow to characterize the structure of invariant states of quantum Markov semigroups having a faithful invariant state. They further provide sufficient conditions for the establishment of environment-induced decoherence, and a method to find decoherence-free subsystems and subspaces. The authors also work out in detail the decoherence-free subalgebra for two examples, namely generic and circulant quantum Markov semigroups.