变值测量结构及其可视化统计分布

利用测量计算模型和系统化参量统计方法模拟双态量子交互作用系统,在多种交互作用模式下模拟双路量子干涉测量的统计分布效应.从量子交互作用出发,对Einstein受激发射,Mach-Zehnder干涉仪和Stern-Gerlach自旋测量等测量模式形成测量四元组.利用多变量逻辑函数和变值原理,在N元0-1输入/输出序对上形成变值测量四元组,建立变值双路模拟模型.变值模型根据:概率、同步/异步、对称/反对称等不同组合条件特征输出统计分布结果,形成2组8个统计直方图.     

在变值测量模拟中的条件概率统计分布

针对常见的两类量子交互干涉实验,Young 氏双缝干涉和超低强度长时间曝光量子交互结果显示出的明显波动统计分布特性,本文基于另一种经典概率测量模型Bayes统计依据的条件概率方法,提出条件概率变值测量模型,建立了测量模拟方法,给出了不同参量的测量公式,并对相关的重要条件进行描述.通过2个具体例子按每个函数形成四组16个...     

变值测量结构及其可视化统计分布

利用测量计算模型和系统化参量统计方法模拟双态量子交互作用系统,在多种交互作用模式下模拟双路量子干涉测量的统计分布效应.从量子交互作用出发,对Einstein受激发射,MachZehnder干涉仪和Stern-Gerlach自旋测量等测量模式形成测量四元组.利用多变量逻辑函数和变值原理,在N元0-1输入/输出序对上形成变...     

无限深势阱中粒子动量概率分布的数值分析

一维无限深势阱中本征态粒子的动量呈现负无穷到正无穷且有无数个节点的对称连续分布.本征态粒子的无量纲动量概率密度分布一般由两个主峰和无数的次峰组成,经典动量和最概然动量都分布在主峰区域内.数值计算结果表明动量谱在两个主峰区域内的概率极限值约为0.902 8,测量所包含的次峰数量越多则粒子出现的概率越接近1.粒子经典动量分布是量子动量分布在高测量精度和大量子数条件下的极限.     

一维晶格中全同任意子的量子动力学与关联

任意子介于玻色子与费米子之间,遵从奇特的分数统计,隐含着许多有趣的物理特性.本文研究了一维晶格中相互作用全同任意子的少体量子动力学及其量子关联性质.基于严格的数值方法,分析了任意子在晶格中局域粒子密度分布的动力学演化过程.结果表明,分数统计可以明显影响任意子动力学演化过程中实空间的局域粒子密度分布,产生新的动力学结构.特别地,当存在相互作用时,分数统计粒子的局域粒子密度分布会呈现有趣的依赖于相互作用性质的不对称性.最后计算了任意子的密度密度关联,分析了粒子统计性质和相互作用对体系量子关联的调制,同时进一步证实了任意子分数统计在实空间中的动力学效应.     

相干瞬态的量子干涉效应和Berry相位

利用解析方法描述了相干瞬态量子体系中不同类型的量子干涉效应,分别讨论了光学干涉与量子干涉所起的作用,分析了在时域对称光场作用下,几何相位在量子干涉效应中所扮演的角色,从理论上证明了通过适当改变抽运场脉冲面积,可实现对几何相位的测量. 同时研究也发现利用啁啾抽运场可以实现对量子干涉效应的有效控制. 关键词： 相干瞬态 量子干涉 几何相位 啁啾脉冲     

基于(2m+1)粒子纠缠态的任意m粒子态量子可控离物传态(英文)

提出了一个基于高维2m+1粒子纠缠态的任意m粒子态量子可控离物传态方案,发送方Alice对需传送的未知态量子系统和手中的纠缠粒子执行m个广义Bell基测量,控制方执行广义X基测量,依据预先共享量子纠缠态非定域相关性,接收方对手中的粒子执行相应的幺正操作就可以重建原来未知量子态.与其他方案相比,方案减少了任意高维多粒子态可控离物传送所需传送粒子数.我们进一步讨论了基于纯纠缠信道的概率量子可控离物传态方案,通过与发送方和控制方合作,接收方只需对手中的纠缠粒子和引入的附加粒子执行联合幺正演化和投影测量,就可以在他的粒子上概率的重建原来的未知量子态,最后,方案计算讨论了基于纯纠缠态量子可控离物传态成功概率与信道纠缠度之间的关系.     

基于InAs单量子点的单光子干涉

利用分子束外延生长 InAs 单量子点样品,测量了温度为 5 K 时单量子点的荧光(PL)光谱.采用时间关联光子强度测量(HBT)验证了 PL 光谱具有单光子发射特性.单光子通过马赫曾德尔 (MZ) 干涉仪,验证了单光子自身具有干涉特性.测量了当 MZ 干涉仪两臂偏振方向的夹角改变时对应的单光子干涉及条纹可见度的变化. 关键词： 量子点单光子源 反群聚效应 马赫曾德尔干涉     

Kerr介质中非关联双模相干态光场与V型三能级原子的相互作用

导出了充满Kerr介质的高Q腔中非关联双模相干态光场与V型三能级原子相互作用系统的态矢量, 通过数值计算,分析了光与原子之间单光子失谐量和Kerr介质对原子能级布居概率及光的量子统计特性的影响,给出了原子布居概率和双模场量子统计特性的时间演化曲线.结果表明, 原子布居概率受Kerr效应的影响较大,且在该曲线上附加一低频起伏. 通过对双模光场二阶相干度的分析:一模呈现亚泊松分布;另一模呈现超泊松分布.     

一种基于积分直方图的粒子滤波跟踪方法

用积分直方图技术提出了一种低复杂度的粒子滤波跟踪方法和基于积分颜色直方图的观测似然模型.采用积分方向直方图建立一个检测响应图,用其上的观测信息构建建议分布函数,在状态空间中似然概率较大的子空间中进行粒子采样.仿真结果表明,在采用大量粒子跟踪大目标时,提出的跟踪方法的计算复杂度明显低于直方图直接提取的粒子滤波方法, 而且在光照变化的条件下,比采用传统颜色Mean-Shift的跟踪方法准确.     

Comparison of Quantum Statistical Models: Equivalent Conditions for Sufficiency

A family of probability distributions (i.e. a statistical model) is said to be sufficient for another, if there exists a transition matrix transforming the probability distributions in the former to the probability distributions in the latter. The Blackwell-Sherman-Stein (BSS) Theorem provides necessary and sufficient conditions for one statistical model to be sufficient for another, by comparing their information values in statistical decision problems. In this paper we extend the BSS Theorem to quantum statistical decision theory, where statistical models are replaced by families of density matrices defined on finite-dimensional Hilbert spaces, and transition matrices are replaced by completely positive, trace-preserving maps (i.e. coarse-grainings). The framework we propose is suitable for unifying results that previously were independent, like the BSS theorem for classical statistical models and its analogue for pairs of bipartite quantum states, recently proved by Shmaya. An important role in this paper is played by statistical morphisms, namely, affine maps whose definition generalizes that of coarse-grainings given by Petz and induces a corresponding criterion for statistical sufficiency that is weaker, and hence easier to be characterized, than Petz’s.     

Conditional expectations,conditional distributions,anda posteriori ensembles in generalized probability theory

A general probabilistic framework containing the essential mathematical structure of any statistical physical theory is reviewed and enlarged to enable the generalization of some concepts of classical probability theory. In particular, generalized conditional probabilities of effects and conditional distributions of observables are introduced and their interpretation is discussed in terms of successive measurements. The existence of generalized conditional distributions is proved, and the relation to M. Ozawa'sa posteriori states is investigated. Examples concerning classical as well as quantum probability are discussed.     

Representation Theorem of Observables on a Quantum System

An orthomodular lattice (OML) with a conditional state can be used as a model for noncompatible events (a quantum system). In this paper we will study some properties of a conditional state and an s-map which are defined on an OML. We show conditions when a quantum system has the same properties as the classical probability space.     

An Approach to Quantum Mechanics via Conditional Probabilities

The well-known proposal to consider the Lüders-von Neumann measurement as a non-classical extension of probability conditionalization is further developed. The major results include some new concepts like the different grades of compatibility, the objective conditional probabilities which are independent of the underlying state and stem from a certain purely algebraic relation between the events, and an axiomatic approach to quantum mechanics. The main axioms are certain postulates concerning the conditional probabilities and own intrinsic probabilistic interpretations from the very beginning. A Jordan product is derived for the observables, and the consideration of composite systems leads to operator algebras on the Hilbert space over the complex numbers, which is the standard model of quantum mechanics. The paper gives an expository overview of the results presented in a series of recent papers by the author. For the first time, the complete approach is presented as a whole in a single paper. Moreover, since the mathematical proofs are already available in the original papers, the present paper can dispense with the mathematical details and maximum generality, thus addressing a wider audience of physicists, philosophers or quantum computer scientists.     

Modeling of the Kinetics of Intramolecular Processes and Transient Spectra with Allowance for Nonradiative Transitions

It has been shown that the kinetics of intramolecular processes and time-resolved spectra with allowance for the quantum beats of the resonant states of isomers or isolated subsystems of levels of one isomeric form can be described with the use of a molecular model interpreting the effect of beats as a nonradiative transition. We have obtained an expression for the nonradiative transition probability, which is directly proportional to the beat frequency and depends oscillatorily on time, thus modeling the effect of beats. The parameter of the molecular system model is the beat frequency directly related to the parameter characterizing the intramolecular interisomeric interactions (the corresponding nondiagonal element of the energy matrix) rather than the value of the nonradiative transition probability. The character of the change in the level populations and, accordingly, in the band intensities in the spectra in the proposed model is in good agreement with the experiment, including the fine structure of the time dependences — oscillations of the line intensities. In analyzing the temporal experiment with a high resolution, it is necessary to take into account the instrument function leading to quantitative and qualitative changes in the time dependences. The traditional model of nonradiative transitions with a constant probability value has a very limited range of applicability — very high beat frequencies compared to the probability of optical transitions.     

Quantum walk under coherence non-generating channels

We investigate the probability distribution of the quantum walk under coherence non-generating channels. We definea model called generalized classical walk with memory. Under certain conditions, generalized classical random walk withmemory can degrade into classical random walk and classical random walk with memory. Based on its various spreadingspeed, the model may be a useful tool for building algorithms. Furthermore, the model may be useful for measuring thequantumness of quantum walk. The probability distributions of quantum walks are generalized classical random walkswith memory under a class of coherence non-generating channels. Therefore, we can simulate classical random walkand classical random walk with memory by coherence non-generating channels. Also, we find that for another class ofcoherence non-generating channels, the probability distributions are influenced by the coherence in the initial state of thecoin. Nevertheless, the influence degrades as the number of steps increases. Our results could be helpful to explore therelationship between coherence and quantum walk.     

From a 1D Completed Scattering and Double Slit Diffraction to the Quantum-Classical Problem for Isolated Systems

By probability theory the probability space to underlie the set of statistical data described by the squared modulus of a coherent superposition of microscopically distinct (sub)states (CSMDS) is non-Kolmogorovian and, thus, such data are mutually incompatible. For us this fact means that the squared modulus of a CSMDS cannot be unambiguously interpreted as the probability density and quantum mechanics itself, with its current approach to CSMDSs, does not allow a correct statistical interpretation. By the example of a 1D completed scattering and double slit diffraction we develop a new quantum-mechanical approach to CSMDSs, which requires the decomposition of the non-Kolmogorovian probability space associated with the squared modulus of a CSMDS into the sum of Kolmogorovian ones. We adapt to CSMDSs the presented by Khrennikov (Found. Phys. 35(10):1655, 2005) concept of real contexts (complexes of physical conditions) to determine uniquely the properties of quantum ensembles. Namely we treat the context to create a time-dependent CSMDS as a complex one consisting of elementary (sub)contexts to create alternative subprocesses. For example, in the two-slit experiment each slit generates its own elementary context and corresponding subprocess. We show that quantum mechanics, with a new approach to CSMDSs, allows a correct statistical interpretation and becomes compatible with classical physics.     

Macroscopic Time Evolution and MaxEnt Inference for Closed Systems with Hamiltonian Dynamics

MaxEnt inference algorithm and information theory are relevant for the time evolution of macroscopic systems considered as problem of incomplete information. Two different MaxEnt approaches are introduced in this work, both applied to prediction of time evolution for closed Hamiltonian systems. The first one is based on Liouville equation for the conditional probability distribution, introduced as a strict microscopic constraint on time evolution in phase space. The conditional probability distribution is defined for the set of microstates associated with the set of phase space paths determined by solutions of Hamilton’s equations. The MaxEnt inference algorithm with Shannon’s concept of the conditional information entropy is then applied to prediction, consistently with this strict microscopic constraint on time evolution in phase space. The second approach is based on the same concepts, with a difference that Liouville equation for the conditional probability distribution is introduced as a macroscopic constraint given by a phase space average. We consider the incomplete nature of our information about microscopic dynamics in a rational way that is consistent with Jaynes’ formulation of predictive statistical mechanics, and the concept of macroscopic reproducibility for time dependent processes. Maximization of the conditional information entropy subject to this macroscopic constraint leads to a loss of correlation between the initial phase space paths and final microstates. Information entropy is the theoretic upper bound on the conditional information entropy, with the upper bound attained only in case of the complete loss of correlation. In this alternative approach to prediction of macroscopic time evolution, maximization of the conditional information entropy is equivalent to the loss of statistical correlation, and leads to corresponding loss of information. In accordance with the original idea of Jaynes, irreversibility appears as a consequence of gradual loss of information about possible microstates of the system.