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Hierarchical remote preparation of equatorial states has practical applications but has not been studied before. We first propose a deterministic protocol for two-dimensional equatorial states via a four-qubit cluster state. The sender can asymmetrically transmit the secret state to any one of the three agents who are ranked in terms of their authorities. A set of useful measurement bases is elaborately constructed which plays a key role in the protocol. Then the protocol is generalized to high-dimensional system. Further, taking advantage of cluster state's symmetry, we give a universal protocol with multiple agents. The high-grade agent needs the assistance of the remaining high-grade agents as well as one of the low-grade agents. While the low-grade agent needs the cooperation of all the other agents. The agents' recovery operators are expressed by a general formula which clearly reveals the relationship with the measurement results. Additionally, the impact of two kinds of noise is analyzed. [ABSTRACT FROM AUTHOR]

Wang et al. first studied hierarchical quantum information splitting of an arbitrary single-qubit state via the χ state as the entangled channel. There exists a hierarchy among the three receivers as far as the power to recover the teleported state is concerned. But the scheme is considered in ideal environment. In this paper, we reinvestigate the scheme in amplitude-damping and phase-damping noises. The fidelity and average fidelity are adopted to quantify the effect of noise. It is found that they are both dependent on the coefficients of the teleported state and the noise parameter. Moreover, we put forward a novel deterministic scheme to realize hierarchical controlled remote preparation of an arbitrary single-qubit state. Comparing with the previous scheme via the χ state, the sender does not need to perform information dividing due to the subtly constructed measurement basis. We also consider the proposed scheme under noisy environment. [ABSTRACT FROM AUTHOR]

Two novel schemes via different entanglement resources are put forward to remotely preparing a five-qubit Brown-type state with high probabilities. To design the schemes, some useful measurement bases with the aid of Hurwitz matrix equation are constructed, which have no restrictions on the coefficients of the prepared state. Through a four-particle projective measurement and two-step three-particle projective measurement under the novel sets of mutually orthogonal basis vectors, the remote preparation can be realized with the probability 50% and 100% in general case, respectively. To improve the probability, the special ensembles of the prepared state that the success probability reaches up to 100% are discussed for the first scheme by the permutation group. Furthermore, the present schemes are extended to the nonmaximally entangled quantum channel. [ABSTRACT FROM AUTHOR]

We propose a deterministic and faithful scheme for realizing the assisted clone of an unknown two-particle entangled state. The first stage of the protocol requires teleportation via maximal entanglement. In the second stage, a novel set of mutually orthogonal basis vectors is constructed. With the assistance of the preparer through a two-particle projective measurement under this basis, a perfect copy of an original state can be produced. Compared with the previous protocols which produce the unknown state and its orthogonal complement state at the site of the sender, our scheme generates the unknown state deterministically. On the other hand, we put forward another assisted clone scheme via nonmaximal entanglement as the quantum channel. A faithful copy of the unknown state can be obtained with a certain probability. [ABSTRACT FROM AUTHOR]

In this paper, an objective reduction approach (a special conditional reduction approach) is presented. As a concrete application in nonlinear physical system, new types of variable separation solutions (including solitary wave solutions, periodic wave solutions, and rational function solutions) with arbitrary functions for the (2+1)-dimensional modified dispersive long-wave system are derived via the objective reduction approach. As special reduction cases based on the derived variable separation solutions, it is shown that some localized coherent structures like nonpropagating and propagating solitons with physical meaning exist in the (2+1)-dimensional modified dispersive long-wave system by prescribing different values of the arbitrary parameters in this short note. [ABSTRACT FROM AUTHOR]

Based on the tight-binding model of the single electron, the one-dimensional Anderson model with random binary distributed on-site energies is studied using the transfer-matrix approach. We calculate numerically the localization length, the density of the electronic states and the Lyapunov exponent. The results show that the localization length strongly depends on energies and is affected by disordered degrees to some extent. With finite size systems, the localization length presents obvious effect on the impurity concentration. While in the dilute limit there exist extended states, increasing the impurity concentration beyond a critical value destroys these extended states and the localization length over the entire energy range becomes smaller than the system size. By studying the scaling relation, we find that the localized states are stable in the thermodynamic limit. Transforming the random matrix product into a conformal map, we introduce the Lyapunov exponent, which is finite within the entire band in our model. Starting from the Lyapunov exponent, the localization length and the density of states may also be obtained. [ABSTRACT FROM AUTHOR]