Decoherence free subspaces of a quantum Markov semigroup

Abstract

We give a full characterisation of decoherence free subspaces of a given quantum Markov semigroup with generator in a generalised Lindbald form which is valid\ud also for infinite-dimensional systems. Our results, extending those available in the literature concerning finite-dimensional systems, are illustrated by some examples

Structure of uniformly continuous quantum Markov semigroups

“…In this section we apply our results to the study of environment induced decoherence ( [8,12,30,31]) and to the identification of subsystems of an open quantum system which are not affected by decoherence ( [3,27,29,35]).…”

Divisibility and coherence properties of an open quantum system: role of the interaction with the environment

“…Hence no decoherence will be observable in this case. Compared with the preceding example the present interaction term contains a degeneracy of states of the system which explains the non-decoherent behaviour of the system [36,37].…”

“…a) Structure of the interaction and consequences Consider now the case where the Hamiltonian Ĥ = ĤS + ĤE + ĤSE is constrained to ĈHSE = [ ĤS , ĤSE ] = 0 like above but with a different form of the interaction which reads [36,37] ĤSE = λ ĝλ ⊗ êλ (46) where ĝλ and êλ are operators acting respectively in H S and H E Hilbert spaces such that the eigenvectors | ĩ of g λ are degenerate with eigenvalue a λ for each term λ.…”

Decoherence-Free Subspaces for Open Quantum Random Walks on Graphs

“…We present the result in the bounded case. (General result is founded in [1], proposition 7 ). Theorem 2.…”

“…As a result, this method cannot be extended to infinite dimensions, or to the case of continuous spectra and unbounded coefficients of the GKSL-generator. In [1] they look at the decoherence-free subspace issue from a mathematical point of view and study the following problem: given a quantum Markov semigroup on the algebra B(h) with generator represented in a generalised GKSL form, characterising its decoherence-free subspaces for a possibly infinite dimensional Hilbert space h. We use this approach by study decoherence-free subspaces and temporary changes of quantum correlations in COQRWs.…”