Partial wave scattering cross sectionsfor He--HBr collision

A new anisotropic potential is fitted to {\it ab initio} data. The close-coupling approach is utilized to calculate state-to-state rotational excitation partial wave cross sections for elastic and inelastic collisions of He atom with HBr molecule based on the fitted potential. The calculation is performed separately at the incident energies: 75, 100 and 200~meV.The tendency of the elastic and inelastic rotational excitation partial wave cross sections varying with total angular quantum number $J$ is obtained.     

Partial evolution based local adiabatic quantum search

Recently, Zhang and Lu provided a quantum search algorithm based on partial adiabatic evolution, which beats the time bound of local adiabatic search when the number of marked items in the unsorted database is larger than one. Later, they found that the above two adiabatic search algorithms had the same time complexity when there is only one marked item in the database. In the present paper, following the idea of Roland and Cerf [Roland J and Cerf N J 2002 Phys. Rev. A 65 042308], if within the small symmetric evolution interval defined by Zhang et al., a local adiabatic evolution is performed instead of the original “global” one, this “new” algorithm exhibits slightly better performance, although they are progressively equivalent with M increasing. In addition, the proof of the optimality for this partial evolution based local adiabatic search when M=1 is also presented. Two other special cases of the adiabatic algorithm obtained by appropriately tuning the evolution interval of partial adiabatic evolution based quantum search, which are found to have the same phenomenon above, are also discussed.     

Partial Boolean Functions With Exact Quantum Query Complexity One

We provide two sufficient and necessary conditions to characterize any n-bit partial Boolean function with exact quantum query complexity 1. Using the first characterization, we present all n-bit partial Boolean functions that depend on n bits and can be computed exactly by a 1-query quantum algorithm. Due to the second characterization, we construct a function F that maps any n-bit partial Boolean function to some integer, and if an n-bit partial Boolean function f depends on k bits and can be computed exactly by a 1-query quantum algorithm, then F(f) is non-positive. In addition, we show that the number of all n-bit partial Boolean functions that depend on k bits and can be computed exactly by a 1-query quantum algorithm is not bigger than an upper bound depending on n and k. Most importantly, the upper bound is far less than the number of all n-bit partial Boolean functions for all efficiently big n.     

Partial Exactness for the Penalty Function of Biconvex Programming

Biconvex programming (or inequality constrained biconvex optimization) is an important model in solving many engineering optimization problems in areas like machine learning and signal and information processing. In this paper, the partial exactness of the partial optimum for the penalty function of biconvex programming is studied. The penalty function is partially exact if the partial Karush–Kuhn–Tucker (KKT) condition is true. The sufficient and necessary partially local stability condition used to determine whether the penalty function is partially exact for a partial optimum solution is also proven. Based on the penalty function, an algorithm is presented for finding a partial optimum solution to an inequality constrained biconvex optimization, and its convergence is proven under some conditions.     

Approximate Noether-Type Symmetries and Conservation Laws via Partial Lagrangians for Nonlinear Wave Equation with Damping

In terms of our new exact definition of partial Lagrangian and approximate Euler-Lagrange-type equation, we investigate the nonlinear wave equation with damping via approximate Noether-type symmetry operators associated with partial Lagrangians and construct its approximate conservation laws in general form.     

Partial and unsharp quantum logics

The total and the sharp character of orthodox quantum logic has been put in question in different contexts. This paper presents the basic ideas for a unified approach to partial and unsharp forms of quantum logic. We prove a completeness theorem for some partial logics based on orthoalgebras and orthomodular posets. We introduce the notion of unsharp orthoalgebra and of generalized MV algebra. The class of all effects of any Hilbert space gives rise to particular examples of these structures. Finally, we investigate the relationship between unsharp orthoalgebras, generalized MV algebras, and orthomodular lattices.     

用部分相干光衍射理论研究光栅成像系统

对可用于研究Ｘ射线源光谱特性的光栅成像系统进行了研究，运用部分相干光成理论对系统的成像性质和传递函数进行分析，指出像面上的光强分布正比于光栅复振幅透过率函数的自相关函数的傅里叶变换和光源在接收面上的几何投影像之间的卷积，并进一步救是光栅成像系统的传递函数正比于光栅率的自相关函数。     

Darboux Transformations of Bispectral Quantum Integrable Systems

We present an approach to higher-dimensional Darboux transformations suitable for application to quantum integrable systems and based on the bispectral property of partial differential operators. Specifically, working with the algebro-geometric definition of quantum integrability, we utilize the bispectral duality of quantum Hamiltonian systems to construct nontrivial Darboux transformations between completely integrable quantum systems. As an application, we are able to construct new quantum integrable systems as the Darboux transforms of trivial examples (such as symmetric products of one dimensional systems) or by Darboux transformation of well-known bispectral systems such as quantum Calogero–Moser.     

Partial Measurements and the Realization of Quantum-Mechanical Counterfactuals

We propose partial measurements as a conceptual tool to understand how to operate with counterfactual claims in quantum physics. Indeed, unlike standard von Neumann measurements, partial measurements can be reversed probabilistically. We first analyze the consequences of this rather unusual feature for the principle of superposition, for the complementarity principle, and for the issue of hidden variables. Then we move on to exploring non-local contexts, by reformulating the EPR paradox, the quantum teleportation experiment, and the entanglement-swapping protocol for the situation in which one uses partial measurements followed by their stochastic reversal. This leads to a number of counter-intuitive results, which are shown to be resolved if we give up the idea of attributing reality to the wavefunction of a single quantum system.     

一个基于三粒子部分纠缠态的量子广播多重盲签名协议

最近有研究者提出了一个基于三粒子最大纠缠态GHZ态的量子广播多重盲签名协议,它能满足一个重要消息需要多人签发,但出于隐私保护要求每一个签名者都不能获取消息的具体内容这一应用需求,并有望应用于电子银行系统.本文给出了一个基于三粒子部分纠缠态的量子广播多重盲签名协议,与原协议相比,该协议用三粒子部分纠缠态代替三粒子极大纠缠GHZ态,并且能不降低协议的安全性.新协议不再依赖于极大纠缠态,仅仅需要在通信参与者之间分享部分纠缠态就可以完成该签名方案,这在一定程度上节约了纠缠资源,降低了协议的实现条件,提高了协议的可应用性.这也充分体现了多体部分纠缠态也可以作为一种量子资源来实现既定的量子通信任务.     

Partial Hermitian Conjugate Separability Criteria for Pure Quantum States

We propose a criterion for the separability of quantum pure states using the concept of a partial Hermitian conjugate. It is equivalent to the usual positive partial transposition criteria, with a simple physical interpretation.     

Partial structures and compressibilities of ions in fused potassium bromide

Treating the coulomb interaction between ion species as a perturbation on the Waisman-Lebowitz solution for direct correlation function within the hard core region, the total direct correlation function in K-space has been formulated, which gives a direct method of evaluating the partial structure factors between different ion species of the fused salts through the use of Pearson-Rushbrooke equations. The partial structure factors so obtained have been applied to evaluate the partial radial distribution functions of ion pairs. In addition, many other important associated functions such as the static correlations of total number, mass and charge densities have been computed by particular linear combination of partial structure factors. The charge neutrality relate the partial structure factors to the isothermal compressibility for the wavevectorK → 0 and hence the evaluation of the compressibilities of ions in fused KBr is possible, which agrees well with the observed value. As such the present method is very useful in investigating the structure of molten salts since only the parametersσ _ij , the distances of closest approach between ions andɛ, the effective dielectric constant (which can be estimated from the literature) are enough for this work.     

Algebraic dynamics solutions and algebraic dynamics algorithm for nonlinear partial differential evolution equations of dynamical systems

Using functional derivative technique in quantum field theory, the algebraic dynamics approach for solution of ordinary differential evolution equations was generalized to treat partial differential evolution equations. The partial differential evolution equations were lifted to the corresponding functional partial differential equations in functional space by introducing the time translation operator. The functional partial differential evolution equations were solved by algebraic dynamics. The algebraic dynamics solutions are analytical in Taylor series in terms of both initial functions and time. Based on the exact analytical solutions, a new numerical algorithm—algebraic dynamics algorithm was proposed for partial differential evolution equations. The difficulty of and the way out for the algorithm were discussed. The application of the approach to and computer numerical experiments on the nonlinear Burgers equation and meteorological advection equation indicate that the algebraic dynamics approach and algebraic dynamics algorithm are effective to the solution of nonlinear partial differential evolution equations both analytically and numerically. Supported by the National Natural Science Foundation of China (Grant Nos. 10375039, 10775100 and 90503008), the Doctoral Program Foundation of the Ministry of Education of China, and the Center of Nuclear Physics of HIRFL of China     

New Solutions of Three Nonlinear Space- and Time-Fractional Partial Differential Equations in Mathematical Physics

Motivated by the widely used ansätz method and starting from the modified Riemann-Liouville derivative together with a fractional complex transformation that can be utilized to transform nonlinear fractional partial differential equations to nonlinear ordinary differential equations, new types of exact traveling wave solutions to three important nonlinear space- and time-fractional partial differential equations are obtained simultaneously in terms of solutions of a Riccati equation. The results are new and first reported in this paper.     

Continuity and Stability of Partial Entropic Sums

Extensions of Fannes’ inequality with partial sums of the Tsallis entropy are obtained for both the classical and quantum cases. The definition of kth partial sum under the prescribed order of terms is given. Basic properties of introduced entropic measures and some applications are discussed. The derived estimates provide a complete characterization of the continuity and stability properties in the refined scale. The results are also reformulated in terms of Uhlmann’s partial fidelities.     

A Novel Quantum Broadcasting Multiple Blind Signature Scheme Based on Multi-Particle Partial Entanglement

Recently, a quantum broadcasting multiple blind signature scheme has been proposed by using GHZ entanglement, which is claimed to have foreseeable application in E-bank system. However, its security is promised by the utilized hash function. In this paper, we have designed a novel quantum broadcasting multiple blind signature scheme by utilizing a three-particle partial entanglement state. In existed quantum broadcasting multiple blind signature schemes, the collector Charlie has to verify the individual signatures before aggregating them into a multi-signature. In this new scheme, Charlie is only acting as a signature collector. Specifically, Charlie only needs to collect all the individual signatures and aggregating them into a multi-signature, which indicates that Charlie has no need to verify the individual signature any more. All the verification are executed by the receiver Bob himself. Meanwhile, the signature is generated by quantum entanglement swapping rather than using hash function, which make its security is only based on quantum physics. It is showed that multi-particle partially entangled state can be efficiently used as a resource in quantum information processing with perfect performance.

     

Implementation of quantum partial search with superconducting quantum interference device qudits in cavity QED

We present a method to implement the quantum partial search of the database separated into any number of blocks with qudits,D-level quantum systems.Compared with the partial search using qubits,our method needs fewer iteration steps and uses the carriers of the information more economically.To illustrate how to realize the idea with concrete physical systems,we propose a scheme to carry out a twelve-dimensional partial search of the database partitioned into three blocks with superconducting quantum interference devices(SQUIDs)in cavity QED.Through the appropriate modulation of the amplitudes of the microwave pulses,the scheme can overcome the non-identity of the cavity–SQUID coupling strengths due to the parameter variations resulting from the fabrication processes.Numerical simulation under the influence of the cavity and SQUID decays shows that the scheme could be achieved efficiently within current state-of-the-art technology.     

Partial Steerability and Nonlocality of Multipartite Quantum States

International Journal of Theoretical Physics - In this paper, we discuss partial steerability and nonlocality of multipartite quantum states. For a state ρ of an n-partite system...     

Strategies for Positive Partial Transpose (PPT) States in Quantum Metrologies with Noise

Quantum metrology overcomes standard precision limits and has the potential to play a key role in quantum sensing. Quantum mechanics, through the Heisenberg uncertainty principle, imposes limits on the precision of measurements. Conventional bounds to the measurement precision such as the shot noise limit are not as fundamental as the Heisenberg limits, and can be beaten with quantum strategies that employ ‘quantum tricks’ such as squeezing and entanglement. Bipartite entangled quantum states with a positive partial transpose (PPT), i.e., PPT entangled states, are usually considered to be too weakly entangled for applications. Since no pure entanglement can be distilled from them, they are also called bound entangled states. We provide strategies, using which multipartite quantum states that have a positive partial transpose with respect to all bi-partitions of the particles can still outperform separable states in linear interferometers.