aqora

Markov quantum semigroups admit covariant MarkovC*-dilations

Jean-Luc Sauvageot

Communications in Mathematical PhysicsMar 1, 198635 citations

Quantum Markov semigroups for continuous-time open quantum random walk

Yuan Bao Kang

Quantum Information ProcessingMay 13, 20194 citations

Quantum Markov Semigroups and Quantum Markov Flows

Franco Fagnola

Jan 1, 199925 citations

Characterization of Gaussian Quantum Markov Semigroups

Damiano Poletti

Springer proceedings in mathematics & statisticsJan 1, 20224 citations

Covariant Ergodic Quantum Markov Semigroups via Systems of Imprimitivity

Radhakrishnan Balu

We construct relativistic quantum Markov semigroups from covariant completely positive maps.We proceed by generalizing a step in Stinespring's dilation to a general system of imprimitivity and basing it on Poincareé group.The resulting noise channels are relativistically consistent and the method is applicable to any fundamental particle, though we demonstrate it for the case of light-like particles.The Krauss decomposition of the relativistically consistent completely positive identity preserving maps (our set up is in Heisenberg picture) enables us to construct the covariant quantum Markov semigroups that are uniformly continuous.We induce representations from the little groups to ensure the quantum Markov semigroups that are ergodic due to transitive systems imprimitivity.We construct relativistic quantum Markov semigroups from covariant completely positive maps.We proceed by generalizing a step in Stinespring's dilation to a general system of imprimitivity and basing it on Poincareé group.The resulting noise channels are relativistically consistent and the method is applicable to any fundamental particle, though we demonstrate it for the case of light-like particles.The Krauss decomposition of the relativistically consistent completely positive identity preserving maps (our set up is in Heisenberg picture) enables us to construct the covariant quantum Markov semigroups that are uniformly continuous.We induce representations from the little groups to ensure the quantum Markov semigroups that are ergodic due to transitive systems imprimitivity.

arXiv:2102.09984Journal of Stochastic AnalysisNov 11, 20211 citation

Structure of covariant uniformly continuous Quantum Markov Semigroups

Nicolò Ginatta

In this thesis I analyze the structure of decoherence-free subalgebra N(T) of a uniformly continuous covariant Quantum Markov Semigroup (QMS) with respect to a representation ? of a compact group G on a Hilbert space h. In particular, I obtain that, when ? is irreducible, N(T) is isomorphic to (?(k) ? 1m)^d for suitable Hilbert spaces k and m, and an integer d related to the connected components of G. I extend this result when ? is reducible and N(T) is atomic by the decomposition of h due to the Peter?Weyl theorem. The thesis is then concluded by exploring the possibility of extending these results beyond the direct sum by using the concept of direct integral.In this thesis I analyze the structure of decoherence-free subalgebra N(T) of a uniformly continuous covariant Quantum Markov Semigroup (QMS) with respect to a representation ? of a compact group G on a Hilbert space h. In particular, I obtain that, when ? is irreducible, N(T) is isomorphic to (?(k) ? 1m)^d for suitable Hilbert spaces k and m, and an integer d related to the connected components of G. I extend this result when ? is reducible and N(T) is atomic by the decomposition of h due to the Peter?Weyl theorem. The thesis is then concluded by exploring the possibility of extending these results beyond the direct sum by using the concept of direct integral.

May 28, 20210 citations

Covariant Uniformly Continuous Quantum Markov Semigroups

Related papers

Covariant Uniformly Continuous Quantum Markov Semigroups

Related papers