On perturbations of dynamical semigroups defined by covariant completely positive measures on the semi-axis

Covariant Quantum Dynamical Semigroups: Unbounded generators

A survey of the probabilistic approaches to quantum dynamical semigroups with unbounded generators is given. An emphasis is made upon recent advances in the structural theory of covariant Markovian master equations. The relations with the classical Levy-Khinchin formula are elucidated. As an example, a complete characterizations of the Galilean covariant irreversible quantum Markovian evolutions is given in terms of the corresponding quantum master and Langevin equations. Important topics for future investigation are outlined.

Covariant Ergodic Quantum Markov Semigroups via Systems of 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 Poincaré 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…

关于由协变测度扰动的量子动力学半群所诱导演化中的态重构

On reconstruction of states from evolution induced by quantum dynamical semigroups perturbed by covariant measures

本文提出利用协变算子值测度扰动量子动力学半群的方法，通过构造受扰半群的积分表示实现经由量子信道（如光纤）传输的量子态重构，并给出Fock空间及经典振子等物理实例。

相位协变非单值量子比特映射的混合

Phase-covariant mixtures of non-unital qubit maps

研究相位协变非单值量子比特映射的凸组合，探讨非单值通道混合如何恢复单值性，以及交换映射混合导致非交换性，证明经典不确定性不破坏量子马尔可夫性。

量子比特Schwarz映射半群弛豫速率的普适约束

Universal constraint for relaxation rates of semigroups of qubit Schwarz maps

本文证明了单比特Schwarz映射半群的弛豫速率满足普适约束，修正了完全正半群的已知约束，并为该映射的谱提供了普适约束及马尔可夫性的必要条件。

Operators versus functions: from quantum dynamical semigroups to tomographic semigroups

Quantum mechanics can be formulated in terms of phase-space functions, according to Wigner's approach. A generalization of this approach consists in replacing the density operators of the standard formulation with suitable functions, the so-called generalized Wigner functions or (group-covariant) tomograms, obtained by means of group-theoretical methods. A typical problem arising in this context is to express the evolution of a quantum system in terms of tomograms. In the case of a (suitable) open quantum system, the dynamics can be described by means of a quantum dynamical semigroup 'in disgu…