LOCALIZATION OPERATORS ASSOCIATED WITH THE SPHERICAL MEAN OPERATOR

In this paper, we define the localization operator associated with the spherical mean operator, and show that the localization operator is not only bounded, but also in Schatten-Von Neumann class. We also give a trace formula when the symbol function is a nonnegative function.

Reproducing Spaces and Localization Operators

This paper, by using of windowed Fourier transform (WFT), gives a family of embedding operators , s.t. are reproducing subspaces (n = 0, Bargmann Space); and gives a reproducing kernel and an orthonormal basis (ONB) of T n L 2(R). Furthermore, it shows the orthogonal spaces decomposition of . Finally, by using the preceding results, it shows the eigenvalues and eigenfunctions of a class of localization operators associated with WFT, which extends the result of Daubechies in [1] and [6].

TWO WEIGHT CHARACTERIZATIONS FOR THE MULTILINEAR LOCAL MAXIMAL OPERATORS

Let 0<β<1 andΩbe a proper open and non-empty subset of R^(n).In this paper,the object of our investigation is the multilinear local maximal operator Mβ,defined by M_(β)((f))(x)=sup_(Q(∈)xQ∈Fβ)Π_(i=1)^m1/|Q|∫_(Q)|f_(i)(y_(i))|dy_(i),where F_(β)={Q(x,l):x∈Ω,l<βd(x,Ω^(c))},Q=Q(x,l)is denoted as a cube with sides parallel to the axes,and x and l denote its center and half its side length.Two-weight characterizations for the multilinear local maximal operator M_(β)are obtained.A formulation of the Carleson embedding theorem in the multilinear setting is proved.

Locally Defined Operators and Locally Lipschitz Composition Operators in the Space WBVp(·)([a, b])

We give a neccesary and sufficient condition on a function such that the composition operator (Nemytskij Operator) H defined by acts in the space and satisfies a local Lipschitz condition. And, we prove that every locally defined operator mapping the space of continuous and bounded Wiener p(&#183;)-variation with variable exponent functions into itself is a Nemytskij com-position operator.

ON THE LOCAL NIKOLSKII CONSTANTS FOR BASKAKOV OPERATORS

In this paper we obtain all other local Nikolskii constants for Baskakov operators by ap- plying a method of asymptotic expansions,give a complete and satisfactory solution of Lehnhoff s open problems[1].

A New Extrapolation Economy Cascadic Multigrid Method for Image Restoration Problems

In this paper, a new extrapolation economy cascadic multigrid method is proposed to solve the image restoration model. The new method combines the new extrapolation formula and quadratic interpolation to design a nonlinear prolongation operator, which provides more accurate initial values for the fine grid level. An edge preserving denoising operator is constructed to remove noise and preserve image edges. The local smoothing operator reduces the influence of staircase effect. The experiment results show that the new method not only improves the computational efficiency but also ensures good recovery quality.

Quantum Secure Direct Communication Network with Two-Step Protocol

An efficient quantum secure direct communication network protocol with the two-step scheme is proposed by using the Einstein-Podolsky-Rosen （EPR） pair block as the quantum information carrier. The server, say Alice, prepares and measures the EPR pairs in the quantum communication and the users perform the four local unitary operations to encode their message. Anyone of the legitimate users can communicate another one on the network securely. Since almost all of the instances in this scheme are useful and each EPR pair can carry two bits of information, the efficiency for qubits and the source capacity both approach the maximal values.

Efficient Multiparty Quantum Secret Sharing with Greenberger-Horne-Zeilinger States

An effcient multiparty quantum secret sharing scheme is proposed with Greenberger-Horne-Zeilinger （GHZ） states following some ideas in quantum dense coding. The agents take the single-photon measurements on the photons received for eavesdropping check and exploit the four local unitary operations Ⅰ, σx, σx and iσy to code their message. This scheme has the advantage of high capacity as each GHZ state can carry two bits of information. The parties do not need to announce the measuring bases for almost all the photons, which will reduce the classical information exchanged largely. The intrinsic efficiency for qubits and the total effciency both approach the maximal values.

Classical Communication and Entanglement Cost in Preparing a Class of Multi-qubit States

Recently, several similar protocols [J. Opt. B 4 （2002） 380; Phys. Lett. A 316 （2003） 159; Phys. Lett. A 355 （2006） 285; Phys. Lett. A 336 （2005） 317] for remotely preparing a class of multi-qubit states （i.e, α[0...0〉 ＋β[1... 1〉） were proposed, respectively. In this paper, by applying the controlled-not （CNOT） gate, a new simple protocol is proposed for remotely preparing such class of states. Compared to the previous protocols, both classical communication cost and required quantum entanglement in our protocol are remarkably reduced. Moreover, the difficulty of identifying some quantum states in our protocol is also degraded. Hence our protocol is more economical and feasible.

Measurement-Device-Independent Quantum Key Distribution with Two-Way Local Operations and Classical Communications

Measurement-device-independent quantum key distribution （MDI-QKD） is proven to be immune to all the de- tector side channel attacks. With two symmetric quantum channels, the maximal transmission distance can be doubled when compared with the prepare-and-measure QKD. An interesting question is whether the transmission distance can be extended further. In this work, we consider the contributions of the two-way local operations and classical communications to the key generation rate and transmission distance of the MDI-QKD. Our numerical results show that the secure transmission distances are increased by about 12kin and 8 km when the 1 13 and the 2 B steps are implemented, respectively.

Entanglement Distillation for Mixed States Using Particle Statistics

We extend the idea of entanglement concentration protocol for pure states （Phys. Rev. Lett. 88, 187903） to the case of entanglement distillation for mixed states. The scheme works only with particle statistics and local operations, without the need of any other interactions. We show that the maximally entangled state can be distilled out when the initial state is pure, otherwise the entanglement distilled depends on the off-diagonal element of density matrix of the initial state. Because of the requirement for density matrix, the entanglement distilled is always less than one, and this result is the same for both fermionic and bosonic particles. The distillation efficiency is a product of the diagonal elements of the initial state, it takes the maximum 50%, the same as that in the case for pure states.We extend the idea of entanglement concentration protocol for pure states （Phys. Rev. Lett. 88, 187903） to the case of entanglement distillation for mixed states. The scheme works only with particle statistics and local operations, without the need of any other interactions. We show that the maximally entangled state can be distilled out when the initial state is pure, otherwise the entanglement distilled depends on the off-dlagonal element of density matrix of the initial state. Because of the requirement for density matrix, the entanglement distilled is always less than one, and this result is the same for both fermionic and bosonic particles. The distillation effciency is a product of the diagonal elements of the initial state, it takes the maximum 50%, the same as that in the case for pure states.

Face Recognition on Partial and Holistic LBP Features

An algorithm for face description and recognition based on multi-resolution with multi-scale local binary pattern （multi-LBP） features is proposed. The facial image pyramid is constructed and each facial image is divided into various regions from which partial and holistic local binary patter （LBP） histograms are extracted. All LBP features of each image are concatenated to a single LBP eigenvector with different resolutions. The dimensionaUty of LBP features is then reduced by a local margin alignment （LMA） algorithm based on manifold, which can preserve the between-class variance. Support vector machine （SVM） is applied to classify facial images. Extensive experiments on ORL and CMU face databases clearly show the superiority of the proposed scheme over some existed algorithms, especially on the robustness of the method against different facial expressions and postures of the subjects.

Classification of Bipartite and Tripartite Qutrit Entanglement Under SLOCC

We classify biqutrit and triqutrit pure states under stochastic local operations and classical communication. By investigating the right singular vector spaces of the coefticient matrices of the states, we obtain explicitly two equivalent classes of biqutrit states and twelve equivalent classes of triqutrit states respectively.

Quantum Dialogue by Using Non-Symmetric Quantum Channel

A protocol for quantum dialogue is proposed to exchange directly the communicator＇s secret messages by using a three-dimensional Bell state and a two-dimensional Bell state as quantum channel with quantum superdence coding, local collective unitary operations, and entanglement swapping. In this protocol, during the process of trans- mission of particles, the transmitted particles do not carry any secret messages and are transmitted only one time. The protocol has higher source capacity than protocols using symmetric two-dimensional states. The security is ensured by the unitary operations randomly performed on all checking groups before the particle sequence is transmitted and the application of entanglement swapping.

Tracking topological entity changes in 3D collaborative modeling systems

One of the key problems in collaborative geometric modeling systems is topological entity correspondence when topolog- ical structure of geometry models on collaborative sites changes, ha this article, we propose a solution for tracking topological entity alterations in 3D collaborative modeling environment. We firstly make a thorough analysis and detailed categorization on the altera- tion properties and causations for each type of topological entity, namely topological face and topological edge. Based on collabora- tive topological entity naming mechanism, a data structure called TEST （Topological Entity Structure Tree） is introduced to track the changing history and current state of each topological entity, to embody the relationship among topological entities. Rules and algo- rithms are presented for identification of topological entities referenced by operations for correct execution and model consistency. The algorithm has been verified within the prototype we have implemented with ACIS.

Noiseless Linear Amplification with General Local Unitary Operations

Noiseless linear amplification （NLA）, first proposed by Ralpha et al., is a nondeterministic amplification process which gives gain to the Fock state ｜n） → gn｜n）, with g being the amplification gain. We here give a general frame- work for improving the NLA scheme with arbitrary general local unitary operations. We derive the improvement in the amplification gain in 0 1 photon subspace. In particular, we study if the local unitary is composed of sin- gle mode squeezing and coherent displacement operation. Finally, numerical simulations show that local unitary operation could give a further enhancement in the amplification gain as well as the success probability, making the NLA more feasible in future optic quantum communications.

Multiparty Quantum Secret Report

A multiparty quantum secret report scheme is proposed with quantum encryption. The boss Alice and her M agents first share a sequence of （M ＋ 1）-particle Greenberger-Horne-Zeilinger （GHZ） states that only Alice knows which state each （M ＋ 1）-particle quantum system is in. Each agent exploits a controlled-not （CNot） gate to encrypt the travelling particle by using the particle in the GHZ state as the control qubit. The boss Alice decrypts the travelling particle with a CNot gate after performing a aσ∞ operation on her particle in the GHZ state or not. After the GHZ states （the quantum key） are used up, the parties check whether there is a vicious eavesdropper, say Eve, monitoring the quantum line, by picking out some samples from the GHZ states shared and measuring them with two measuring bases. After confirming the security of the quantum key, they use the remaining GHZ states repeatedly for the next round of quantum communication. This scheme has the advantage of high intrinsic efficiency for the qubits and total efficiency.

Simplified Four-Qubit Cluster State for Splitting Arbitrary Single-Qubit Information

The simplified four-qubit cluster state （i.e., （｜0000〉 ＋ ｜0011〉 ＋ ｜1100〉 -｜1111〉）/2） is explored for splitting an arbitrary single-qubit quantum information （QI）. Various feasible distributions of the four qubits among the Q,I sender and receivers for tri-splitting or hi-splitting are found out. For the distribution representations the corresponding splitting schemes and their LOCCs （local operation and classical communication） are presented amply while others are mentioned concisely.

Three-Party Quantum State Sharing of an Arbitrary Unknown Two-Qubit State Based on Entanglement Swapping and Bell-State Measurements

We propose a scheme for sharing an arbitrary unknown two-qubit state among three parties by using afour-qubit cluster-class state and a Bell state as a quantum channel With a quantum controlled phase gate (QCPG)operation and a local unitary operation,any one of the two agents has the access to reconstruct the original state ifhe/she collaborates with the other one,whilst individual agent obtains no information.As all quantum resource canbe used to carry the useful information,the intrinsic efficiency of qubits approaches the maximal value.Moreover,thepresent scheme is more feasible with present-day technique.

Two-Step Deterministic Remote Preparation of an Arbitrary Quantum State

We present a two-step deterministic remote state preparation protocol for an arbitrary qubit with the aid of a three-particle Greenberger-Horne-Zeilinger state. Generalization of this protocol for higher-dimensional Hilbert space systems among three parties is also given. We show that only single-particle yon Neumann measurements, local operations, and classical communication are necessary. Moreover, since the overall information of the quantum state can be divided into two different pieces, which may be at different locations, this protocol may be useful in the quantum information field.