Pairwise entanglement in symmetric multi-qubit systems

For pairs of particles extracted from a symmetric state of N two-level systems, the two-particle density matrix is expressed in terms of expectation values of collective spin operators for the large system. Results are presented for experimentally relevant examples of pure states: Dicke states | S, M>, spin coherent, and spin squeezed states, where only the symmetric subspace, S = N/2 is populated, and for thermally entangled mixed states populating also lower S values. The entanglement of the extracted pair is then quantified by a calculation of the concurrence, which provides directly the entanglement of formation of the pair. Received 9 May 2001 and Received in final form 16 November 2001     

Decomposition of pure states of quantum register

The generalization of Schmidt decomposition due to Cartelet-Higuchi-Sudbery applied to quantum register (a system of N qubits) is shown to acquire direct geometrical meaning: any pure state is canonically associated with a chain of a simplicial complex. A leading vector method is presented to calculate the values of the coefficients of appropriate chain.     

On general properties of cubic systems

This paper develops the analytical solutions of non‐trivial examples of a well‐known class of initial‐boundary value problems which, by the choice of parameters, can be reduced to regular or singular Sturm‐Liouville problems. The examples could be used in lecture notes, in tutorial problems or to help evaluate numerical methods.     

Investigating and comparing the dynamic patterns of the business value of information technology over time

The long-debated issue of the business value of information technology (IT) to the firm (country) has received a great deal of attention in the literature. But the studies have rarely examined the dynamic patterns of the IT value as measured by the firm’s productive efficiency over time. The objective of this paper is to apply the three-factor constant elasticity of substitution (CES) time-varying stochastic production frontier models and use the same data set as used in several previous studies to investigate the dynamic patterns of IT value over time in connection with the issues of inputs substitution and complement and the productivity paradox. This paper adopts two analytical skills, collective and individual, to analyze the empirical results. Collectively, we find that the dynamic patterns of IT value are closely related to the substitution and complement of three inputs and the IT productivity paradox. Individually, we identify five common dynamic patterns of the IT value measured by productive efficiency and interpret their implications for the productivity paradox as summarized in a two by two matrix of practical applications and strategies. This matrix accounts for four different scenarios of the relationship between the average productive efficiency and the IT productivity paradox, illustrates some practical applications by the analytical results, and provides some business insights and managerial strategies for IT decision makers and PO/IS managers. This represents a new contribution to the understanding of the dynamic influence of IT investments upon the value of IT over time.     

Trouton–Noble Paradox Revisited

An apparent paradox is obtained in all previous treatments of the Trouton–Noble experiment; there is a three-dimensional (3D) torque T in an inertial frame S in which a thin parallel-plate capacitor is moving, but there is no 3D torque T′ in S′, the rest frame of the capacitor. Different explanations are offered for the existence of another 3D torque, which is equal in magnitude but of opposite direction giving that the total 3D torque is zero. In this paper, it is considered that 4D geometric quantities and not the usual 3D quantities are well-defined both theoretically and experimentally in the 4D spacetime. In analogy with the decomposition of the electromagnetic field F (bivector) into two 1-vectors E and B we introduce decomposition of the 4D torque N (bivector) into 1-vectors N _s , N _t . It is shown that in the frame of “fiducial” observers, in which the observers who measure N _s and N _t are at rest, and in the standard basis, only the spatial components and remain, which can be associated with components of two 3D torques T and T _t . In such treatment with 4D geometric quantities the mentioned paradox does not appear. The presented explanation is in complete agreement with the principle of relativity and with the Trouton–Noble experiment without the introduction of any additional torque.     

Entanglement in the three-qubit Heisenberg model with next nearest neighbor interaction and a nonuniform magnetic field

Pairwise thermal entanglement in the three-qubit XXX Heisenberg model with next nearest neighbor interaction and a nonuniform magnetic field has been studied. It's found that the next nearest neighbor interaction has a great effect on the entanglement between the next nearest neighbor sites, but has slight effect on the nearest neighbor entanglement (NNE). Applying a magnetic field at the middle site enhances the next nearest neighbor entanglement (NNNE) sharply when there is a small field at the side sites and the next nearest neighbor coupling constant is positive. A staggered magnetic field helps to maintain nearest neighbor entanglement obviously.     

Random delayed-choice quantum eraser via two-photon imaging

We report on a delayed-choice quantum eraser experiment based on a two-photon imaging scheme using entangled photon pairs. After the detection of a photon which passed through a double-slit, a random delayed choice is made to erase or not erase the which-path information by the measurement of its distant entangled twin; the particle-like and wave-like behavior of the photon are then recorded simultaneously and respectively by only one set of joint detection devices. The present eraser takes advantage of two-photon imaging. The complete which-path information of a photon is transferred to its distant entangled twin through a “ghost" image. The choice is made on the Fourier transform plane of the ghost image between reading “complete information" or “partial information" of the double-path.     

基于变构学习模型的高中化学“导致悖论”教学设计*

“导致悖论”教学是一种智在创境、妙在引领的教学,其核心理念源自于变构学习模型的悖论思想,给学习者创造一个“肯定→否定→肯定”的反思性学习过程。高中化学教学设计可以通过4种途径分别创设“概念与概念”相悖、“理论与实验”相悖、“理论与理论”相悖和“实验与实验”相悖的悖论情境,最终实现学生新旧概念的更替和高阶思维能力的发展。“导致悖论”教学在实施中要注意精选合适的知识内容,加强学生心理的调控,提供丰富的支撑材料。     

Pointwise optimality of Bayesian wavelet estimators

We consider pointwise mean squared errors of several known Bayesian wavelet estimators, namely, posterior mean, posterior median and Bayes Factor, where the prior imposed on wavelet coefficients is a mixture of an atom of probability zero and a Gaussian density. We show that for the properly chosen hyperparameters of the prior, all the three estimators are (up to a log-factor) asymptotically minimax within any prescribed Besov ball . We discuss the Bayesian paradox and compare the results for the pointwise squared risk with those for the global mean squared error.     

Dissipation-induced instabilities and symmetry

The paradox of destabilization of a conservative or non-conservative system by small dissipation,or Ziegler’s paradox(1952),has stimulated a growing interest in the sensitivity of reversible and Hamiltonian systems with respect to dissipative perturbations.Since the last decade it has been widely accepted that dissipation-induced instabilities are closely related to singularities arising on the stability boundary,associated with Whitney’s umbrella.The first explanation of Ziegler’s paradox was given(much earlier)by Oene Bottema in 1956.The aspects of the mechanics and geometry of dissipation-induced instabilities with an application to rotor dynamics are discussed.