量子纠缠和量子计算

量子纠缠是量子力学中的一种非经典现象。本文从介绍纠缠和纠缠态出发,着重讨论纠缠的本质和非定域性概念。文末还讨论了纠缠在量子计算中的作用：它是量子计算优于经典计算的重要原因之一。     

Analysis of non-local image denoising methods

Image denoising is probably one of the most studied problems in the image processing community. Recently a new paradigm on non-local denoising was introduced. The non-local means method proposed by Buades, Morel and Coll computes the denoised image as a weighted average of pixels across the whole image. The weight between pixels is based on the similarity between neighborhoods around them. This method attracted the attention of other researchers who proposed improvements and modifications to it. In this work we analyze those methods trying to understand their properties while connecting them to segmentation based on spectral properties of the graph that represents the similarity of neighborhoods of the image. We also propose a method to automatically estimate the parameters which produce the optimal results in terms of mean square error and perceptual quality.     

基于FDH包围盒的布料碰撞检测

在布料仿真中,碰撞检测与响应十分复杂,很难同时具备真实感和实时性。针对此问题,采用质点弹簧模型进行建模,基于FDH包围盒提出一种快速的检测基本几何元素间碰撞的方法。通过分析点的位置向量与三角平面的夹角,利用向量内积的性质来判断点与三角形的位置关系,同时进行了相应的碰撞响应处理。实验结果表明,采用该方法进行碰撞检测既保证了模拟的真实性,同时又提高了系统的实时性。     

Remotely Prepared Entanglement: a Quantum Web Page

Abstract. In quantum teleportation, an unknown quantum state is transmitted from one party to another using only local operations and classical communication, at the cost of shared entanglement. Is it possible similarly, using an N party entangled state, to have the state retrievable by any of the N-1 possible receivers? If the receivers cooperate, and share a suitable state, this can be done reliably. The N party GHZ is one such state; I derive a large class of such states, and show that they are in general not equivalent to the GHZ. I also briefly discuss the problem where the parties do not cooperate, and the relationship to multipartite entanglement quantification. I define a new set of entanglement monotones, the entanglements of preparation.     

Adaptive feature-preserving non-local denoising of static and time-varying range data

We present a new method for noise removal on static and time-varying range data. Our approach predicts the restored position of a perturbed vertex using similar vertices in its neighborhood. It defines the required similarity measure in a new non-local fashion which compares regions of the surface instead of point pairs. This allows our algorithm to obtain a more accurate denoising result than previous state-of-the-art approaches and, at the same time, to better preserve fine features of the surface. Another interesting component of our method is that the neighborhood size is not constant over the surface but adapted close to the boundaries which improves the denoising performance in those regions of the dataset. Furthermore, our approach is easy to implement, effective, and flexibly applicable to different types of scanned data. We demonstrate this on several static and interesting new time-varying datasets obtained using laser and structured light scanners.     

Management of personal safety risk for lever operation in mechanical railway signal boxes

Despite increased implementation of computer control systems in managing and regulating rail networks, mechanical signal boxes using lever operation will be in place for years to come. A rolling risk assessment programme identified a number of levers in mechanical signal boxes within the UK rail network which potentially presented unacceptable personal safety risk to signallers. These levers operate both points and signals and the risk is primarily the weights which have to be moved when pulling and pushing the levers. Operating difficulties are often compounded by the design and condition of lever frames, the linkages to the points/signals, maintenance regimes, the workspace and the postures and strategies adopted by signallers. Lever weights were measured as from 15 kg to 180 kg at over 160 boxes, using a specially designed and constructed device. Taken together with examination of injury and sickness absence data, interviews and field observations, and biomechanical computer modelling, the measurement programme confirmed the potential risks. A risk management programme has been implemented, comprising lever weight measurement, training of operations staff, a structured maintenance regime and renewal or redesign for boxes/levers where, after maintenance, a criterion weight level is still exceeded. For a feasible management programme, the first alert (or 1st action) value for further assessment is 55 kg, a second action level requiring specified maintenance is 80–99 kg, and a third action level requiring the lever to be signed out of use is 100 kg.     

Construction of families of probability boxes and corresponding membership functions at different fractiles

Uncertainty comes in many forms in the real world and is an unavoidable component of human life. Generally, two types of uncertainties arise, namely, aleatory and epistemic uncertainty. Probability is a well established mathematical tool to handle aleatory uncertainty and fuzzy set theory is a tool to handle epistemic uncertainty. However, in certain situations, parameters of probability distributions may be tainted with epistemic uncertainty; and so, representation of parameters of probability distributions may be treated as fuzzy numbers (may be of different shapes). A probability box (P‐box) can be constructed when parameters are not precisely known. In this paper, an attempt has been made to construct families of P‐boxes when parameters of probability distributions are bell shaped or normal fuzzy numbers; and from these families of P‐boxes, membership functions are generated at different fractiles for different alpha levels.     

Modelling of elastoplastic behaviour with non-local damage in concrete under compression

In the first part, an elastoplastic damage model is proposed for concrete under compression-dominated stresses. The model is applied to typical concrete in various loading conditions. The model’s parameters are determined from conventional triaxial tests. The comparison between experimental data and numerical simulations shows the performance of the model in predicting basic mechanical behaviour of concrete for a large range of stress. In the second part, an extension of the model is proposed by including a non-local damage formulation. The extended model is applied to the analysis of failure process zone in concrete related to material softening behaviour.     

Controllability for a class of integro-differential evolution equations involving non-local initial conditions

This paper deals with the exact controllability for a class of first-order integro-differential evolution equations involving non-local initial conditions. By using Sadovskii fixed point theorem, exact controllability results are obtained without assuming the compactness and Lipschitz conditions for non-local functions. An example is given to illustrate the effectiveness of the abstract results.     

Controlled teleportation against uncooperation of part of supervisors

We study the teleportation of an unknown quantum state from a sender (Alice) to a receiver (Bob) via the control of many supervisors (Charlie 1, Charlie 2, . . .) in a network. It has been shown that such a task can be achieved by distributing a GHZ-type entangled state among the participants in advance. In the protocols with GHZ-type entanglement channel, the achievement of teleportation between Alice and Bob is conditioned on the cooperation of all the supervisors. In other words, if anyone of the supervisors does not cooperate, the teleportation will fails. In this paper, we introduce another kind of controlled teleportaton protocol with other types of entangled states acting as the quantum channel, in which the teleportation between Alice and Bob can be realized with high degree of endurance against uncooperation of part of supervisors.      

Entanglement assisted classical capacity of a class of quantum channels with long-term memory

In this paper we evaluate the entanglement assisted classical capacity of a class of quantum channels with long-term memory, which are convex combinations of memoryless channels. The memory of such channels can be considered to be given by a Markov chain which is aperiodic but not irreducible. This class of channels was introduced by Datta and Dorlas in (J. Phys. A, Math. Theor. 40:8147–8164, 2007), where its product state capacity was evaluated.      

Self-adaptive sampling rate assignment and image reconstruction via combination of structured sparsity and non-local total variation priors

Compressive sensing (CS) is an emerging approach for acquisition of sparse or compressible signals. For natural images, block compressive sensing (BCS) has been designed to reduce the size of sensing matrix and the complexity of sampling and reconstruction. On the other hand, image blocks with varying structures are too different to share the same sampling rate and sensing matrix. Motivated by this, a novel framework of adaptive acquisition and reconstruction is proposed to assign sampling rate adaptively. The framework contains three aspects. First, a small part of sampling rate is employed to pre-sense each block and a novel approach is proposed to estimate its compressibility only from pre-sensed measurements. Next, two assignment schemes are proposed to assign the other part of the sampling rate adaptively to each block based on its estimated compressibility. A higher sampling rate is assigned to incompressible blocks but a lower one to compressible ones. The sensing matrix is constructed based on the assigned sampling rates. The pre-sensed measurements and the adaptive ones are concatenated to form the final measurements. Finally, it is proposed that the reconstruction is modeled as a multi-objects optimization problem which involves the structured sparsity and the non-local total variation prior together. It is simplified into a 3-stage alternating optimization problem and is solved by an augmented Lagrangian method. Experiments on four categories of real natural images and medicine images demonstrate that the proposed framework captures local and nonlocal structures and outperforms the state-of-the-art methods.     

The Feynman tools for quantum information processing: Design and implementation

The Feynman tools have been re-designed with the goal to establish and implement a high-level (computer) language that is capable to deal with the physics of finite, n$n$-qubit systems, from frequently required computations to mathematically advanced tasks in quantum information processing. In particular, emphasis has been placed to introduce a small but powerful set of keystring-driven commands in order to support both, symbolic and numerical computations. Though the current design is implemented again within the framework of Maple, it is general and flexible enough to be utilized and combined with other languages and computational environments. The present implementation facilitates a large number of computational tasks, including the definition, manipulation and parametrization of quantum states, the evaluation of quantum measures and quantum operations, the evolution of quantum noise in discrete models, quantum measurements and state estimation, and several others. The design is based on a few high-level commands, with a syntax close to the mathematical notation and its use in the literature, and which can be generalized quite readily in order to solve computational tasks at even higher degree of complexity.     

Quantum scholasticism: On quantum contexts, counterfactuals, and the absurdities of quantum omniscience

Unlike classical information, quantum knowledge is restricted to the outcome of measurements of maximal observables corresponding to single contexts.     

On non-local stability properties of extremum seeking control

In this paper, we consider several extremum seeking schemes and show under appropriate conditions that these schemes achieve extremum seeking from an arbitrarily large domain of initial conditions if the parameters in the controller are appropriately adjusted. This non-local stability result is proved by showing semi-global practical stability of the closed-loop system with respect to the design parameters. We show that reducing the size of the parameters typically slows down the convergence rate of the extremum seeking controllers and enlarges the domain of the attraction. Our results provide guidelines on how to tune the controller parameters in order to achieve extremum seeking. Simulation examples illustrate our results.     

建立液压系统信息模型的研究

所设计的液压系统信息模型将液压系统分作系统、元件和油口3个层次，以多层链表的方式将其连接起来，能简单地与液压系统一一对应。而使用液压系统信息模型的整个仿真系统也分为3层，以信息模型为核心，向上层映射为数学模型，向下层映射到数据库。研究结果表明：所采用的体系结构弹性足，构造灵活，不但能满足液压仿真的需要，而且对系统的扩展性、对多方应用间信息集成都有着良好的支持。     

Quantum Information and the PCP Theorem

Our main result is that the membership x∈SAT (for x of length n) can be proved by a logarithmic-size quantum state |Ψ〉, together with a polynomial-size classical proof consisting of blocks of length polylog(n) bits each, such that after measuring the state |Ψ〉 the verifier only needs to read one block of the classical proof. This shows that if a short quantum witness is available then a (classical) PCP with only one query is possible. Our second result is that the class QIP/qpoly contains all languages. That is, for any language L (even non-recursive), the membership x∈L (for x of length n) can be proved by a polynomial-size quantum interactive proof, where the verifier is a polynomial-size quantum circuit with working space initiated with some quantum state |Ψ _L,n 〉 (depending only on L and n). Moreover, the interactive proof that we give is of only one round, and the messages communicated are classical. The advice |Ψ _L,n 〉 given to the verifier can also be replaced by a classical probabilistic advice, as long as this advice is kept as a secret from the prover. Our result can hence be interpreted as: the class IP/rpoly contains all languages. For the proof of the second result, we introduce the quantum low-degree-extension of a string of bits. The main result requires an additional machinery of quantum low-degree-test. R. Raz’s research was supported by Israel Science Foundation (ISF) grant.     

电网规划指标的相关性分析及融合算法

目前决策指标体系中,大多忽略了指标的相关性问题,这将影响整个电网规划的可靠性、经济性。针对指标决策中不确定性问题,提出一种基于概率盒理论的指标相关性分析模型及融合算法。首先对指标采用Lucas模型进行相关性分析;然后对相关性的指标建立概率盒,并根据相关系数进行概率盒融合;最后利用重叠因子进行定量分析。以某省电网规划方案的底层指标为例进行了实验,结果表明,该方法对解决相关性及其融合问题具有良好的实效性和精准度。