非交换概率上的马尔可夫转移

B（h）对称和量子细致平衡下KMS对称马氏半群的生成元

Generators of KMS Symmetric Markov Semigroups on B(h) Symmetry and Quantum Detailed Balance

本文给出了B（h）上关于标积树对称的范数连续量子马氏半群的生成元的结构（ρ^{1/2}xρ^{1/2}y）由一个忠实的正常不变态诱导不变态ρ，并满足与这种非对易对称性概念相关的经典细致平衡条件的两个量子推广：所谓的标准细致平衡条件和具有反酉时间反演的标准细致平衡条件。

2D Schrödinger Equation with Singular Even-Power and Inverse-Power Potentials in Non Commutative Complex space

We obtain exact solutions of the 2D Schrödinger equation with the Singular Even-Power and Inverse-Power Potentials in non-commutative complex space, using the Power-series expansion method. Hence we can say that the Schrödinger equation in non-commutative complex space describes to the particles with spin (1/2)in an external uniform magnitic field. Where the noncommutativity play the role of magnetic field with created the total magnetic moment of particle with spin 1/2, who in turn shifted the spectrum of energy. Such effects are similar to the Zeeman splitting in a commutative space.

Non-commutative Nash inequalities

A set of functional inequalities - called Nash inequalities - are introduced and analyzed in the context of quantum Markov process mixing. The basic theory of Nash inequalities is extended to the setting of non-commutative Lp spaces, where their relationship to Poincare and log-Sobolev inequalities are fleshed out. We prove Nash inequalities for a number of unital reversible semigroups.

高斯量子马尔可夫生成元的谱隙

The Spectral Gap of a Gaussian Quantum Markovian Generator

本文研究高斯量子马尔可夫半群生成元的谱隙，在忠实不变密度下显式给出其由扩散与漂移矩阵决定的精确值，并比较 GNS 与 KMS 两类非对易 $L^2$ 空间。

通过近似环境使非马尔可夫主方程易于处理

Making Non-Markovian master equations accessible with approximate environments

研究开放量子系统非马尔可夫动力学模拟难题，核心方法是将环境关联函数表示为阻尼正弦波之和，主要贡献是降低计算成本、简化兰姆移位修正计算，在弱耦合 regime 精度与数值精确方法相当，简化加速了模拟。

Suppression of ac Stark shift scattering rate due to non-Markovian behavior

The ac Stark shift in the presence of spontaneous decay is typically considered to induce an effective dephasing with a scattering rate equal to $ Γ_s |Ω|^2/Δ^2 $, where $ Γ_s $ is the spontaneous decay rate, $ Ω$ is the laser transition coupling, and $ Δ$ is the detuning. We show that under realistic circumstances this dephasing rate may be strongly modifed due to non-Markovian behavior. The non-Markovian behavior arises due to an effective modification of the light-atom coupling in the presence of the ac Stark shift laser. An analytical formula for the non-Markovian ac Stark shift induced de…

Quantum extensions of dynamical systems and of Markov semigroups

We investigate some particular completely positive maps which admit a stable commutative Von Neumann subalgebra. The restriction of such maps to the stable algebra is then a Markov operator. In the first part of this article, we propose a recipe in order to find a quantum extension of a given Markov operator in the above sense. We show that the existence of such an extension is linked with the existence of a special form of dilation for the Markov operator studied by Attal in \cite{Att1}, reducing the problem to the extension of dynamical system. We then apply our method to the same problem in…

量子相对熵γ族的一般形式

The general form of gamma-family of quantum relative entropies

我们使用Falcone-Takesaki非交换流的权重和由此产生的理论的非交换Lp空间，以定义家庭的相对熵泛函，自然概括的量子相对熵的Jencova大岛和经典的相对熵的朱Rohwer，属于交叉家庭的Petz相对熵与布雷格曼相对熵。为了这项任务的目的，我们推广的概念Bregman熵的无限维非交换的情况下使用Legendre-Fenchel对偶。此外，我们还利用Falcone-Takesaki对偶将粗粒度映射和马尔可夫映射之间的对偶推广到无限维非交换的情形。根据Amari最近关于Zhu-Rohwer熵的结果，我们猜想所提出的相对熵族是唯一的，具有Markov单调性和Legendre-Fenchel对偶性.这些结果的基础和应用的量子信息理论的作用进行了讨论。

双纠缠隐马尔可夫过程与常返性

Bi-Entangled Hidden Markov Processes and Recurrence

本文提出双纠缠隐马尔可夫过程概念，给出其联合期望公式，研究相关量子马尔可夫过程常返性，证明限制于交换子代数可恢复经典隐马尔可夫过程，仅考虑至多可数状态空间。

Deviation bounds and concentration inequalities for quantum noises

We provide a stochastic interpretation of non-commutative Dirichlet forms in the context of quantum filtering. For stochastic processes motivated by quantum optics experiments, we derive an optimal finite time deviation bound expressed in terms of the non-commutative Dirichlet form. Introducing and developing new non-commutative functional inequalities, we deduce concentration inequalities for these processes. Examples satisfying our bounds include tensor products of quantum Markov semigroups as well as Gibbs samplers above a threshold temperature.

Open Quantum Random Walks, Quantum Markov Chains and Recurrence

In the present paper, we construct QMCs associated with Open Quantum Random Walks such that the transition operator of the chain is defined by OQRW and the restriction of QMC to the commutative subalgebra coincides with the distribution $P_ρ$ of OQRW. This sheds new light on some properties of the measure $P_ρ$. As an example, we simply mention that the measure can be considered as a distribution of some functions of certain Markov process. Furthermore, we study several properties of QMC and associated measure. A new notion of $\f$-recurrence of QMC is studied, and it is established relations …

Open Quantum Random Walks and Quantum Markov chains on Trees II: The recurrence

In the present paper, we construct QMC (Quantum Markov Chains) associated with Open Quantum Random Walks such that the transition operator of the chain is defined by OQRW and the restriction of QMC to the commutative subalgebra coincides with the distribution of OQRW. Furthermore, we first propose a new construction of QMC on trees, which is an extension of QMC considered in Ref. [9]. Using such a construction, we are able to construct QMCs on tress associated with OQRW. Our investigation leads to the detection of the phase transition phenomena within the proposed scheme. This kind of phenomen…