Decompositions of Hilbert spaces, stability analysis and convergence probabilities for discrete-time quantum dynamical semigroups

Cirillo Giuseppe Ilario; Ticozzi Francesco

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Decompositions of Hilbert spaces, stability analysis and convergence probabilities for discrete-time quantum dynamical semigroups

机译：离散时间量子动力学半群的希尔伯特空间分解，稳定性分析和收敛概率

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We investigate convergence properties of discrete-time semigroup quantum dynamics, including asymptotic stability, probability and speed of convergence to pure states and subspaces. These properties are of interest in both the analysis of uncontrolled evolutions and the engineering of controlled dynamics for quantum information processing. Our results include two Hilbert space decompositions that allow for deciding the stability of the subspace of interest and for estimating of the speed of convergence, as well as a formula to obtain the limit probability distribution for a set of orthogonal invariant subspaces.

机译：我们研究离散时间半群量子动力学的收敛性质，包括渐近稳定性，收敛到纯态和子空间的概率和速度。这些特性在量子信息处理的不受控制的演化分析和受控制的动力学工程中都令人感兴趣。我们的结果包括两个Hilbert空间分解，这些分解可用来确定感兴趣子空间的稳定性并估计收敛速度，以及一个用于获取一组正交不变子空间的极限概率分布的公式。

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《Journal of physics, A. Mathematical and theoretical》 |2015年第8期|共28页
作者
Cirillo Giuseppe Ilario; Ticozzi Francesco;
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正文语种 eng
中图分类物理学;
关键词
quantum channels; quantum dynamical semigroups; convergence; Perron-Frobenious theory;

机译：量子通道;量子动力学半群;收敛;Perron-Frobenious理论;

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1. Decompositions of Hilbert spaces, stability analysis and convergence probabilities for discrete-time quantum dynamical semigroups [J] . Cirillo Giuseppe Ilario, Ticozzi Francesco Journal of physics, A. Mathematical and theoretical . 2015,第8期

机译：离散时间量子动力学半群的希尔伯特空间分解，稳定性分析和收敛概率
2. ATTRACTIVE POINT AND MEAN CONVERGENCE THEOREMS FOR SEMIGROUPS OF MAPPINGS WITHOUT CONTINUITY IN HILBERT SPACES [J] . Takahashi Wataru, Wong Ngai-Ching, Yao Jen-Chih Journal of nonlinear and convex analysis . 2014,第6期

机译：Hilbert空间中不连续的映射半群的吸引点和均值收敛定理
3. WEAK AND STRONG CONVERGENCE THEOREMS FOR SEMIGROUPS OF MAPPINGS WITHOUT CONTINUITY IN HILBERT SPACES [J] . NAWAB HUSSAIN, WATARU TAKAHASHI Journal of nonlinear and convex analysis . 2013,第4期

机译：Hilbert空间中不连续的映射半群的弱和强收敛定理
4. Convergence Analysis of Penalty Decomposition Algorithm for Cardinality Constrained Convex Optimization in Hilbert Spaces [C] . Michael Pleshakov, Sergei Sidorov, Kirill Spiridonov International Conference on Mathematical Optimization Theory and Operations Research . 2020

机译：Hilbert空间中基数约束凸优化的惩罚分解算法的收敛性分析
5. A multivariate time series analysis based on frequency domain decomposition and Hilbert space projection in the presence of missing data. [D] . Iasonos, Alexia Elia. 2002

机译：在缺少数据的情况下，基于频域分解和希尔伯特空间投影的多元时间序列分析。
6. Quantum dynamics of excitations and decoherence in many-spin systems detected with Loschmidt echoes: its relation to their spreading through the Hilbert space [O] . C. M. Sánchez, P. R. Levstein, L. Buljubasich, -1

机译：用Loschmidt回波检测到的多自旋系统中激发和退相干的量子动力学：与它们在希尔伯特空间中的传播的关系
7. Decompositions of Hilbert Spaces, Stability Analysis and Convergence Probabilities for Discrete-Time Quantum Dynamical Semigroups [O] . Cirillo, Giuseppe Ilario, Ticozzi, Francesco 2015

机译：Hilbert空间的分解，稳定性分析和收敛性离散时间量子动力半群的概率
8. Strong Convergence of Semigroups of Nonlinear Contractions in Hilbert Space. [R] . Pazy, A. 1978

机译：Hilbert空间非线性收缩半群的强收敛性。

Decompositions of Hilbert spaces, stability analysis and convergence probabilities for discrete-time quantum dynamical semigroups

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