An Implementation of a Positive Operator Valued Measure
Feng-Li Yan, Ting Gao, You-Cheng Li
给出了正算子值测度（POVM）的一种实现.利用这种POVM可以实现未知两粒子态的概率隐形传态。
An implementation of the positive operator valued measure (POVM) is given. By using this POVM one can realize the probabilistic teleportation of an unknown two-particle state.
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Positive operator valued measures covariant with respect to an irreducible representation
给定群G的一个不可约表示，证明了所有基于G/Z的协变正算子值测度，其中Z是中心子群，都可用迹类迹1正算子来刻画.
Positive operator valued measures covariant with respect to an Abelian group
给定阿贝尔群$G$和子群$H$的酉表示$U$，我们证明了正算子值商群$G/H$关于$U$的协变.
Kochen-Specker theorem for a single qubit using positive operator-valued measures
给出了单个二能级系统的Kochen-Specker定理的一个证明。它采用了五个八元正算子值的措施和一个简单的代数推理的基础上的几何形状的十二面体。
Symmetric Informationally Complete Positive Operator Valued Measure and Zauner conjecture
本文证明在任意有限维N的Hilbert空间中，存在N^2个单位向量构成对称信息完备正算子值测度（SIC-POVM）。
Experimental Test of the Kochen-Specker Theorem for Single Qubits using Positive Operator-Valued Measures
我们提出了一个实验方案的实施任意广义测量，代表正算子值的措施，对单光子的偏振，使用线性光学器件。此外，我们实验测试的Kochen-Specker定理的单量子比特使用积极的运营商值的措施。我们的实验结果第一次反驳了非上下文隐藏变量理论，即使是单量子比特。
Heisenberg's uncertainty principle for simultaneous measurement of positive-operator-valued measures
讨论了两个任意正算子值测度同时测度的一个限制。一般来说，同时测量两个非对易观测量只是近似可能的。根据维尔纳的公式，我们引入了可观测量之间的距离来量化测量的准确性。我们推导出一个不等式，涉及可达到的精度与两个观测值之间的非交换性。作为副产品，得到了两个正算子值测度同时可测的必要条件。
Positive operator valued measurements (POVMs) play an important role in efficient quantum communication and computation. While optical systems are one of the strongest candidates for long distance quantum communication and information processing, efficient methods to implement POVMs in these systems are scarce. Here we propose an all-optical scheme to implement an arbitrary POVM using linear optical components on m-dimensional Hilbert space of internal degrees of freedom. Linear optical nature of the proposed scheme makes it efficient and robust. We show how the scheme can be applied for state…
Concurrence classes for an arbitrary multi-qubit state based on positive operator valued measure
本文提出了基于量子相位上正算子值测度的正交补（简称POVM）的任意多量子比特态的并发类。特别地，我们构造了任意两个量子比特状态的并发和三个和四个量子比特状态的并发类。最后，我们构造了多比特态的$W^{m}$和$GHZ^{m}$类并发。我们的POVM的独特结构，使我们能够区分不同的并发类的多量子比特状态。
Nonsequential positive-operator-valued measurements on entangled mixed states do not always violate a Bell inequality
我们提出了一个局部隐变量模型的正算子值的测量（LHVWerner模型）的一类纠缠广义Werner态，从而证明了这样的测量并不总是违反贝尔型不等式。我们还表明，在一般情况下，如果状态$ρ'$可以从$ρ$确定性的本地量子操作没有经典的通信，然后一个LHV模型的状态$ρ$意味着存在这样一个模型$ρ'$。
Realization of single-qubit positive operator-valued measurement via a one-dimensional photonic quantum walk
我们通过将量子位实现为光子量子行走中的硬币并使行走者进行投影测量来执行量子位的广义测量。我们的实验技术可以用来实现光子任何秩1单量子比特正算符值测量通过构建一个适当的干涉量子行走网络，然后投影测量的步行者的位置在最后一步。
Geometric approach to extend Landau-Pollak uncertainty relations for positive operator-valued measures
通过几何考虑，我们给出了混合量子态和正算符值测度的Landau-Pollak测不准关系的双重扩展。推广是基于纯状态之间的度量，具有状态之间的内积的平方的函数的形式。这种度量所满足的三角不等式在我们的推导中起着至关重要的作用。通常的朗道-波拉克不等式，因此是一个特殊的情况下（来自Wootters度量）的家庭得到的不等式，而且，我们表明，它是最严格的关系在家庭。
Realization of positive-operator-valued measures by projective measurements without introducing ancillary dimensions
我们提出了一个方案，可以实现一类正算子值的措施（POVM）通过执行一系列的投影测量的原始系统，在这个意义上说，对于任意输入状态的概率分布的测量结果是忠实地再现。一个必要和充分条件的POVM是可实现的，以这种方式也得到了。与Neumark定理所提供的规范方法相比，我们的方法具有不需要辅助系统的优点。此外，一个任意的POVM可以实现通过利用我们的协议在一个扩展的空间，这是通过添加只有一个额外的维形成。
Bridging particle and wave sensitivity in a detector of configurable positive operator-valued measures
我们报道了一种具有可调正算子值测度（POVM）的光探测器。该设备是基于弱场零差技术和光子数分辨检测相结合。通过调节不同的系统参数，如本振耦合、振幅和相位，可以将所得到的POVM从Fock态投影仪连续调谐到各种相位相关的量子态测量，从而不仅允许检测，而且允许制备奇异的量子态。实验断层重建的经典基准状态作为一个示范的检测器的能力。
Minimal sufficient positive-operator valued measure on a separable Hilbert space
我们引入了最小充分正算子值测度（POVM）的概念，它是在具有被测量子系统等价信息的POVM中冗余度最小的POVM.假设系统的希尔伯特空间是可分的，我们证明了，对于一个给定的POVM的一个充分的统计称为莱曼-谢弗-巴哈杜尔统计诱导一个最小的充分POVM。我们还表明，每个POVM有一个等价的最小充分POVM，这样的最小充分POVM是唯一的重新标记忽略空集。我们将这些结果应用于离散POVM和作者提出的信息守恒条件。
Evaluating the amount of information obtained from non-orthogonal quantum states is an important topic in the field of quantum information. The commonly used evaluation method is Holevo bound, which only provides a loose upper bound for quantum measurement. In this paper, we provide a theoretical study of the positive operator-valued measure (POVM) for discriminating nonorthogonal states. We construct a generalized POVM measurement operation, and derive the optimal one for state discrimination by Lagrange multiplier method. With simulation, we find that the optimal POVM measurement provides a …
Clean positive operator valued measures for qubits and similar cases
在最近的一篇论文中，Buscemi等人定义了干净正算子值测度（POVM）的概念。我们在这里描述哪些POVM是干净的，我们称之为准量子比特POVM，即POVM的元素都是秩一或满秩的。我们给出了一个算法来检查给定的准比特POVM是否满足这个条件。我们明确地描述了所有的POVM是干净的量子位。同时给出了一般POVM为clean的一个充分条件。
Positive Operator-Valued Measure reconstruction of a beam-splitter tree based photon-number-resolving detector
在这里，我们提出了一个重建的正算子值测量的光子数分辨探测器组成的三个50：50分束器的树配置，终止于四个单光子雪崩探测器。四个探测器的输出由一个电子板处理，该电子板将探测到的光子数状态从0到4进行区分，并执行“智能计数”程序，以补偿高计数率下的死区时间问题。
We tackle the dynamical description of the quantum measurement process, by explicitly addressing the interaction between the system under investigation with the measurement apparatus, the latter ultimately considered as macroscopic quantum object. We consider arbitrary Positive Operator Valued Measures (POVMs), such that the orthogonality constraint on the measurement operators is relaxed. We show that, likewise the well-known von-Neumann scheme for projective measurements, it is possible to build up a dynamical model holding a unitary propagator characterized by a single time-independent Hami…
Comment on "Uncertainty Relations for Positive Operator Valued Measures"
本评论的主要目的是纠正Massar [arXiv：quant-ph/0703036 v2（当前版本）]在一篇论文中提出的熵不确定性关系，该论文涉及研究POVM产生的噪声的两种方法。接下来要强调的是，由上述作者获得的POVM的第一个熵界已经在参考文献[8]中给出。阐明了评论文章中公式（14）的一些模糊论述。最后，对论文的内容进行了较为具体的评述。
Uncertainty Relations for Positive Operator Valued Measures
一个正算子值测度（POVM）会产生多少不可避免的随机性？我们使用两种互补的方法来解决这个问题。首先，我们研究与POVM结果相关的实变量的方差。在这种情况下，我们引入了一个不确定性算子，它测量有多少额外的噪声引入进行POVM，而不是冯诺依曼测量。我们通过研究自旋为1/2的粒子的σ_x和σ_z的联合估计的方差来说明第一种方法。我们表明，无偏的测量，这些方差的总和是下界1。在第二种方法中，我们研究POVM结果的熵。特别是，我们试图建立POVM结果的熵的下限。我们通过例子来说明第二种方法。
Observables Generalizing Positive Operator Valued Measures
我们讨论了一个推广的POVM，这是用于心理加工的量子建模。
A general symmetric-informationally-complete (GSIC)-positive-operator-valued measure (POVM) is known to provide an optimal quantum state tomography among minimal IC POVMs with a fixed average purity. In this paper we provide a general construction of a GSIC POVM by means of a complete orthogonal basis (COB), also interpreted as a normal quasiprobability representation. A spectral property of a COB is shown to play a key role in the construction of SIC POVMs and also for the bound of the mean-square error of the state tomography. In particular, a necessary and sufficient condition to construct …
We derive a deterministic protocol to implement a general single-qubit POVM on near-term circuit-based quantum computers. The protocol has a modular structure, such that an $n$-element POVM is implemented as a sequence of $(n-1)$ circuit modules. Each module performs a $2$-element POVM. Two variations of the protocol are suggested, one optimal in terms of number of ancilla qubits, the other optimal in terms of number of qubit gate operations and quantum circuit depth. We use the protocol to implement $2$- and $3$-element POVMs on two publicly available quantum computing devices. The results we…
In this paper we present a protocol for the implementation of a positive-operator-valued measure (POVM) on massive fermionic qubits. We present methods for implementing non-dispersive qubit transport, spin rotations and spin polarizing beam-splitter operations. Our scheme attains linear optics-like control of the spatial extent of the qubits by considering groundstate electrons trapped in the minima of surface acoustic waves in semiconductor heterostructures. Furthermore, we numerically simulate a high-fidelity POVM that carries out Procrustean entanglement distillation in the framework of our…
Quantum Implementation of Non-Positive-Operator-Valued Measurements in General Probabilistic Theories by Post-Selected POVMs
本文提出在限制目标态定义域的条件下，利用POVM测量与后选择在量子理论中构造性实现一般概率理论中的N-POVM测量，并证明后选择POVM可视为受限域上的N-POVM，从而建立N-POVM与后选择之间的新联系。
Positive Operation Valued Measurement Based Multi-User Detection in DS-CDMA Systems
3G和4G是基于CDMA技术的移动通信。为了提高CDMA接收机的有效性，人们投入大量的精力来开发合适的多用户检测器技术。然而，目前只有次优的解决方案，因为最佳检测器的复杂性相当高。可能的接收器技术之一可以是量子辅助计算设备，其允许计算中的高级并行性。第一批商用设备预计在2004年，这符合3G和4G系统的广告。本文提出了一种基于量子计算的量子多用户检测算法，该算法采用简单的正操作值测量（POVM），提供了最优解。该算法对任何类型的噪声都具有鲁棒性。
Quantum coherence is a fundamental feature of quantum mechanics and an underlying requirement for most quantum information tasks. In the resource theory of coherence, incoherent states are diagonal with respect to a fixed orthonormal basis, i.e., they can be seen as arising from a von Neumann measurement. Here, we introduce and study a generalization to a resource theory of coherence defined with respect to the most general quantum measurement, i.e., to an arbitrary positive-operator-valued measure (POVM). We establish POVM-based coherence measures and POVM-incoherent operations which coincide…
Bounds on positive operator-valued measure based coherence of superposition
该研究将相干性资源理论推广至POVM测量，解析推导了叠加纯态相干性的上下界，并用示例验证，可用于估计叠加态相干性范围。
We address the problem of quantum nonlocality with positive operator valued measures (POVM) in the context of Einstein-Podolsky-Rosen quantum steering. We show that, given a candidate for local hidden state (LHS) ensemble, the problem of determining the steerability of a bipartite quantum state of finite dimension with POVMs can be formulated as a nesting problem of two convex objects. One consequence of this is the strengthening of the theorem that justifies choosing the LHS ensemble based on symmetry of the bipartite state. As a more practical application, we study the classic problem of the…
Spontaneous parametric down conversion (PDC), in the perturbative limit, can be considered as a probabilistic splitting of one input photon into two output photons. Conversely, sum-frequency generation (SFG) implements the reverse process of combining two input photons into one. Here we show that a single-photon projective measurement in the temporal-mode basis of the output photon of a two-photon SFG process effects a generalized measurement on the input two-photon state. We describe the positive-operator-valued measure (POVM) associated with such a measurement, and show that its elements are…
We mainly study the block-coherence measures based on resource theory of block-coherence and the coherence measures based on positive-operator-valued measures (POVM). Several block-coherence measures including a block-coherence measure based on maximum relative entropy, the one-shot block coherence cost under the maximally block-incoherent operations, and a coherence measure based on coherent rank have been introduced and the relationships between these block-coherence measures have been obtained. We also give the definition of the maximally block-coherent state and describe the deterministic …
We consider positive operator valued measures whose image is the bounded operators acting on an infinite-dimensional Hilbert space, and we relax, when possible, the usual assumption of positivity of the operator valued measure seen in the quantum information theory literature. We define the Radon-Nikodym derivative of a positive operator valued measure with respect to a complex measure induced by a given quantum state; this derivative does not always exist when the Hilbert space is infinite dimensional in so much as its range may include unbounded operators. We define integrability of a positi…
Positive-Operator-Valued Time Observable in Quantum Mechanics
我们研究了长期存在的问题，在量子力学中引入一个时间观测;使用正算子值的措施的形式主义，我们展示了如何定义这样一个观察到一个自然的方式，我们讨论了一些后果。
Extremal covariant positive operator valued measures: the case of a compact symmetry group
给定紧群G的酉表示U和可迁G-空间$Ω$，刻画了所有U-协变正算子值测度的凸集的极值元.
Experimental scheme for qubit and qutrit symmetric informationally complete positive operator-valued measurements using multiport devices
从一般的量子测量中可靠而有效地确定量子系统的状态对于各种量子信息处理任务至关重要。为此目的的一类重要的测量是对称信息完全正算子值测量（SIC-POVM）。SIC-POVM的优点是为量子态提供了一个无偏的估计器，具有完全断层扫描所需的最少数量的结果。根据Naimark膨胀定理，任何POVM总是可以通过系统和辅助系统之间的适当耦合以及通过对联合系统进行投影测量来实现。在实践中，找到适当的耦合是相当重要的。在这里，我们提出了一个实验设计，直接实现SIC-POVM使用多端口设备和路径编码的量子比特和量子，其效用最近已被证明由世界各地的几个实验组。此外，我们描述了如何在实践中实现这些多端口与集成的光子系统嵌套的线性光学元件组成。
Generalized Coherent States and Extremal Positive Operator Valued Measures
给出了正算子值测度（POVM）与广义相干态集之间的对应关系。正算子值测度描述量子可观测量，并且类似于量子态，量子可观测量也可以混合。我们展示了如何广义相干态的形式主义导致一个有用的表征极值POVM。我们证明了与压缩态相关的协变相空间观测量是极值的，而与数态相关的协变相空间观测量不是极值的。
Clean Positive Operator Valued Measures
在量子力学中，测量仪器的结果的统计由正算子值测度（POVM）描述。量子信道通常不可逆地将POVM变换为POVM，从而丢失从测量中检索的一些信息。这就提出了哪些POVM是“未受干扰的”的问题，即它们不是不可逆地连接到另一个POVM。我们称之为干净的POVM。在某种意义上，干净的POVM将是“完美的”，因为它们不会有任何额外的“外在”噪声。出乎意料的是，事实证明，这种清洁性质在很大程度上与POVM的凸结构无关，并且存在清洁的POVM不是极值，反之亦然。在本文中，我们解决了结果数n<=d（希尔伯特空间的d维）的cleannes分类问题，并且我们提供了n>d的一组必要或充分条件，以及n=d^2的信息完全POVM的情况下的一个当条件。
Manipulation of qudits in optical tables is a difficult and nonscalable task. The use of integrated optical circuits opens new possibilities for the generation, manipulation, and characterization of high dimensional states besides the ease of transmission of these states through an optical fiber. In this work we propose photonic circuits to perform minimum quantum state tomography of path qudits and show how to determine all the constituents parameters of these circuits (beam splitters and phase shifters). Our strategies were based on the symmetries of the involved POVMs (positive operator-val…
Quantum resource theories provide a diverse and powerful framework for extensively studying the phenomena in quantum physics. Quantum coherence, a quantum resource, is the basic ingredient in many quantum information tasks. It is a subject of broad and current interest in quantum information, and many new concepts have been introduced and generalized since its establishment. Here we show that the block coherence can be transformed into entanglement via a block incoherent operation. Moreover, we find that the POVM-based coherence associated with block coherence through the Naimark extension act…
Self-Testing Positive Operator-Valued Measurements and Certifying Randomness
本文在设备无关场景下，通过构造贝尔表达式C'3及其变体，自测试三输出极值量子比特POVM，分别认证约1.58比特局部和2.27比特全局随机性，超越投影测量限制，并利用NPA层级验证C3在随机性认证中的优势。
Time-efficient implementation of quantum search with qudits
我们提出了一个更简单，更有效的计划，实现多值Grover的量子搜索。多值搜索通过用qudits -$d$离散态的量子系统来代替qubit来推广原始Grover搜索。qudit数据库比qubit数据库大得多，因此需要控制的粒子更少。Hadamard门是Grover搜索的量子比特实现中的关键基本门，它被一个$d$维（复值）酉矩阵$F$取代，唯一的条件是有一列等模元素，而不管它们的相位如何;它可以通过任何物理相互作用来实现，从而实现等重叠加态。这种变换的一个例子是$d$维离散傅立叶变换，在早期的建议中使用;然而，它的构造比简单得多的矩阵$F$的构造成本高得多。我们目前的例子，这样的转换$F$可以构建在现实的量子系统中的\emph{single}互动步骤。
On constructing informationally complete covariant positive operator-valued measures
本文研究局部紧Abel群投影酉表示轨道生成的正算子值测度，证明其积分定义的收缩算子族为表示中酉算子的倍数，据此证明测度信息完备性，并以相干态密度测度为例验证结果。
Commutative POVMs and Fuzzy Observables
本文讨论了模糊可观量的一些性质，主要是由可交换的正算子值测度实现的。在这方面，我们讨论了两个表示定理的可交换的正算子值的措施，在投影值的措施和描述，在一定程度上详细的模糊化的一般概念。我们还提出了一些联合测量的相关意见。
In Ref. [Phys. Rev. A 100, 062317 (2019)], the authors reported an algorithm to implement, in a circuit-based quantum computer, a general quantum measurement (GQM) of a two-level quantum system, a qubit. Even though their algorithm seems right, its application involves the solution of an intricate non-linear system of equations in order to obtain the angles determining the quantum circuit to be implemented for the simulation. In this article, we identify and discuss a simple way to circumvent this issue and implement GQMs on any $d$-level quantum system through quantum state preparation algori…
Conditions for the existence of positive operator valued measures
本文提出了任意维量子系统中(N,M)-POVMs存在的充分与必要条件，揭示了最优POVMs与特定算子基的联系，并证明了M小于系统维度时其元素必为等秩投影算子，极大限制了构造参数。
Distinguishability of Quantum States by Positive Operator-Valued Measures with Positive Partial Transpose
研究了二分量子态的正部分转置正算符值测度（PPT POVM）可解性。本文的贡献包括：（1）.本文对[M. Horodecki $et. al$，物理学评论快报。90，047902（2003）]，其显示了他们用于检测不可重复性的方法的局限性。（二）、我们发现，一个最大纠缠态和它的正交补，无论有多少副本提供，不能区分PPT POVM，甚至明确。这个结果比以前已知的\cite{DUAN06,BAN11}强得多。（三）、研究了区分量子态的纠缠代价。证明了$\sqrt{2/3}\ket{00}+\sqrt{1/3}\ket{11}$是用PPT POVM区分三种Bell态的充分必要条件。在可分离操作下，得到了区分$d\otimes d$纯态及其正交补态的纠缠代价的上界。基于这个界限，我们可以构造两个正交的量子态，它们不能被可分的POVM明确区分，但是有限的副本可以使它们完全被LOCC区分。我们进一步观察到，无论$d$的值是多少，一个两量子比特的最大纠缠态总是足以区分$d\otimes d$纯态和它的正交补态.与此形成鲜明对比的是，要用可分的POVM区分这两种态，总是需要Schmidt数至少为$d$的纠缠态。作为应用，我们证明了区分$d\otimes d$最大纠缠态和它的正交补态的纠缠代价必须是$d=2$的最大纠缠态，这意味着隐形传态是最优的，一般情况下，它可以被选择为$\mathcal{O}(…
Positive operator-valued measures in quantum decision theory
我们表明，正确的量子决策理论的数学基础，处理不确定的事件，需要使用积极的算子值的措施，是一个推广的投影值的措施。后者适用于作战上可检验的事件，而前者是表征作战上不确定事件所必需的。在决策中，必须区分复合非纠缠事件和复合纠缠事件。纠缠前景的数学定义基于希尔伯特-施密特空间理论，类似于量子信息理论中纠缠统计算子的定义。我们证明了量子概率中出现干涉项的必要条件是纠缠前景的出现和决策者的纠缠策略态的存在。标准彩票的不确定性的起源进行了解释。
Quantifying nonclassicality in qubit systems via positive operator-valued measures
该研究提出基于POVM不锐利度参数的量子比特非经典性度量，推导其显式表达式，最大值为1/4，关联Kolmogorov一致性等，为量子技术认证提供实验工具。
Saving resources through repeat-until-success positive-operator-valued-measure measurements in quantum computation
提出一种基于POVM测量的量子计算方法，通过辅助比特的中间测量实现重复直至成功，可多项式减少量子比特和酉操作数量，节省计算资源。
Covariance Systems on the Projective Line
假设能量为正算子，研究了关于射影群的射影实线协变上的正算子值测度。这个问题类似于在紧化的闵可夫斯基时空协变量上寻找关于共形群的正算子值测度的更复杂的问题。它还描述了一个自由粒子协变的线性正则变换的到达时间观测。
Generalized Landau-Pollak Uncertainty Relation
Landau-Pollak不确定关系处理一对秩一投影值测度，并对它们的概率分布施加限制。它给出了它们的最大值之和的非平凡界。我们给出了这个界的一个推广（弱版本的Landau-Pollak不确定性关系）。我们的推广涵盖了一对正算子值测度。一个非平凡的，但稍弱的不等式，可以处理任意数量的正算子值的措施。
We introduce several notions of random positive operator valued measures (POVMs), and we prove that some of them are equivalent. We then study statistical properties of the effect operators for the canonical examples, obtaining limiting eigenvalue distributions with the help of free probability theory. Similarly, we obtain the large system limit for several quantities of interest in quantum information theory, such as the sharpness, the noise content, and the probability range. Finally, we study different compatibility criteria, and we compare them for generic POVMs.
The modular valued operator $\widehat{V}_m$ of the von Neumann interaction operator for a projector is defined. The properties of $\widehat{V}_m$ are discussed and contrasted with those of the standard modular value of a projector. The associated notion of a faux qubit is introduced and its possible utility in quantum computation is noted. An experimental implementation of $\widehat{V}_m$ is also highlighted.
We show that a partition of the unity (or POVM) on a Hilbert space that is almost orthogonal is close to an orthogonal POVM in the same von Neumann algebra. This generalizes to infinite dimension previous results in matrix algebras by Kempe-Vidick and Ji-Natarajan-Vidick-Wright-Yuen. Quantitatively, our result are also finer, as we obtain a linear dependance, which is optimal. We also generalize to infinite dimension a duality result between POVMs and minimal majorants of finite subsets in the predual of a von Neumann algebra.
Entanglement Criteria Based on Quantum Fisher Information
该研究通过在测量轨道上最大化 QFI 建立可操作纠缠判据，比较两类局部可观测量，证明 SIC-POVM 在纠缠检测中更优。
Constructing Operator Valued Probability Measures in Phase Space
概率测度（准概率质量），以维格纳函数在相空间区域上的积分形式给出，产生了算子值概率测度（OVM）。研究了一般一维域和二维圆、盘等几何正迹增加映射（PTI）的OVM的一般构造方法。讨论了OVM的谱特性及其构造PIT的操作实现。
We introduce positive operator-valued measure (POVM) generated by the projective unitary representation of a direct product of locally compact Abelian group $G$ with its dual $\hat G$. The method is based upon the Pontryagin duality allowing to establish an isometrical isomorphism between the space of Hilbert-Schmidt operators in $L^2(G)$ and the Hilbert space $L^2(\hat G\times G)$. Any such a measure determines a pair of hybrid (containing classical and quantum parts) quantum channels consisting of the measurement channel and the channel transmitting an initial quantum state to the ensemble o…
Classical and nonclassical randomness in quantum measurements
紧的Borel集上的正算子值测度空间通过变换$Γ$，研究了d维Hilbert空间上的Hausdorff空间（甚至局部紧的）的经典和非经典凸性，该变换将任何正算子值测度与齐次C* 的某个完全正线性映射联系起来。将$C(X)\otimes B(H)$代数化为$B(H)$。这种关联是通过使用算子值积分来实现的，其中非经典随机变量（即算子值函数）相对于正算子值测度被积分，并且具有随机量子效应的积分本身就是量子效应的特征。$Γ$的一个左逆$Ω$给出了某些（但不是全部）单位完全正线性映射$ϕ:C(X)\otimes B(H) \rightarrow B(H)$的积分表示，沿着$C(X)$上某些线性泛函的经典Riesz表示定理。确定了POVMS空间的极值点和C*-极值点。
Conditional expectation and Bayes' rule for quantum random variables and positive operator valued measures
一个量子概率测度是一个满足测度形式要求的样本空间子集的sigma-代数上的函数，但其值是作用在复希尔伯特空间上的正算子，量子随机变量是一个可测算子值函数。虽然量子概率测度和随机变量在量子力学中被广泛使用，但这些结构的一些基本概率特征仍有待确定。在本文中，我们采取了一个更好的数学理解量子随机变量和量子概率措施通过引入一个量子模拟的期望值的量子随机变量相对于量子概率措施。在这样做的时候，我们导致定理的变化量子测量和变化的量子变量。我们还引入了一个量子条件期望，这导致在量子版本的Radon-Nikodym衍生物的一些标准的身份。这使我们能够制定和证明贝叶斯规则的量子模拟。
From Classical to Quantum: Polymorphisms in Non-Commutative Probability
本文建立经典（标量值）与非交换（算子值）多态性之间的平行关系，重点应用于随机过程的条件分布，并借助正算子值测度（POVM）与量子态，阐明量子信息中的纠缠，揭示两种框架的相互作用。
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