38,668 research outputs found

    Environment-induced decay of teleportation fidelity of the one-qubit state

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    The one-qubit teleportation protocol is reexamined when it is executed in the presence of various decohering environments. The results revealed that this quantum protocol is more robust under the influence of dephaisng environment than those under the influence of dissipative or noisy environment. The environment may deprive the quantum advantage of teleportation over purely classical communication in a finite or infinite lifetime, which is dependent on the type of environment. Also we found that except entanglement, the purity of the entangled state resource is also crucial in determine the quality of the teleported state.Comment: 10 pages, 2 figure

    Liouville-type theorems for the fourth order nonlinear elliptic equation

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    In this paper, we are concerned with Liouville-type theorems for the nonlinear elliptic equation {equation*} \Delta^2 u=|x|^a |u|^{p-1}u\;\ {in}\;\ \Omega, {equation*}where aβ‰₯0a \ge 0, p>1p>1 and Ξ©βŠ‚Rn\Omega \subset \mathbb{R}^n is an unbounded domain of Rn\mathbb{R}^n, nβ‰₯5n \ge 5. We prove Liouville-type theorems for solutions belonging to one of the following classes: stable solutions and finite Morse index solutions (whether positive or sign-changing). Our proof is based on a combination of the {\it Pohozaev-type identity}, {\it monotonicity formula} of solutions and a {\it blowing down} sequence, which is used to obtain sharper results

    Monotonicity formula and Liouville-type theorems of stable solution for the weighted elliptic system

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    In this paper, we are concerned with the weighted elliptic system \begin{equation*} \begin{cases} -\Delta u=|x|^{\beta} v^{\vartheta},\\ -\Delta v=|x|^{\alpha} |u|^{p-1}u, \end{cases}\quad \mbox{in}\;\ \Omega, \end{equation*}where Ξ©\Omega is a subset of RN\mathbb{R}^N, Nβ‰₯5N \ge 5, Ξ±>βˆ’4\alpha >-4, 0≀β≀Nβˆ’420 \le \beta \le \dfrac{N-4}{2}, p>1p>1 and Ο‘=1\vartheta=1. We first apply Pohozaev identity to construct a monotonicity formula and find their certain equivalence relation. By the use of {\it Pohozaev identity}, {\it monotonicity formula} of solutions together with a {\it blowing down} sequence, we prove Liouville-type theorems of stable solutions for the weighted elliptic system (whether positive or sign-changing) in the higher dimension

    Robustness of Greenberger-Horne-Zeilinger and W states for teleportation in external environments

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    By solving analytically a master equation in the Lindblad form, we study quantum teleportation of the one-qubit state under the influence of different surrounding environments, and compared the robustness between Greenberger-Horne-Zeilinger (GHZ) and W states in terms of their teleportation capacity. The results revealed that when subject to zero temperature environment, the GHZ state is always more robust than the W state, while the reverse situation occurs when the channel is subject to infinite temperature or dephasing environment.Comment: 12 pages, 4 figure

    Bilinear Factorization For Low-Rank SDP Learning

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    Many machine learning problems can be reduced to learning a low-rank positive semidefinite matrix (denoted as ZZ), which encounters semidefinite program (SDP). Existing SDP solvers are often expensive for large-scale learning. To avoid directly solving SDP, some works convert SDP into a nonconvex program by factorizing ZZ quadraticlyquadraticly as XX⊀XX^\top. However, this would bring higher-order nonlinearity, resulting in scarcity of structure in subsequent optimization. In this paper, we propose a novel surrogate for SDP-related learning, in which the structure of subproblem is exploited. More specifically, we surrogate unconstrained SDP by a biconvex problem, through factorizing ZZ bilinearlybilinearly as XY⊀XY^\top and using a Courant penalty to penalize the difference of XX and YY, in which the resultant subproblems are convex. Furthermore, we provide a theoretical bound for the associated penalty parameter under the assumption that the subobjective function is LL-Lipschitz-smooth and Οƒβˆ’\sigma-strongly convex, such that the proposed surrogate will solve the original SDP when the penalty parameter is larger than this bound, that is Ξ³>14(Lβˆ’Οƒ)\gamma>\frac{1}{4}(L-\sigma). Experiments on two SDP-related machine learning applications demonstrate that the proposed algorithm is as accurate as the state-of-the-art, but is faster on large-scale learning

    Collective excitations of a trapped Bose-Einstein condensate in the presence of weak disorder and a two-dimensional optical lattice

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    We investigate the combined effects of weak disorder and a two-dimensional (2D) optical lattice on the collective excitations of a harmonically trapped Bose-Einstein condensate (BEC) at zero temperature. Accordingly, we generalize the hydrodynamic equations of superfluid for a weakly interacting Bose gas in a 2D optical lattice to include the effects of weak disorder. Our analytical results for the collective frequencies beyond the mean-field approximation reveal the peculiar role of disorder, interplaying with the 2D optical lattice and interatomic interaction, on elementary excitations along the 3D to 1D dimensional crossover. In particular, consequences of disorder on the phonon propagation and surface modes are analyzed in detail. The experimental scenario is also proposed.Comment: 11 pages, no figures, accepted for publication in Physical Review

    Dynamic Video Streaming in Caching-enabled Wireless Mobile Networks

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    Recent advances in software-defined mobile networks (SDMNs), in-network caching, and mobile edge computing (MEC) can have great effects on video services in next generation mobile networks. In this paper, we jointly consider SDMNs, in-network caching, and MEC to enhance the video service in next generation mobile networks. With the objective of maximizing the mean measurement of video quality, an optimization problem is formulated. Due to the coupling of video data rate, computing resource, and traffic engineering (bandwidth provisioning and paths selection), the problem becomes intractable in practice. Thus, we utilize dual-decomposition method to decouple those three sets of variables. Extensive simulations are conducted with different system configurations to show the effectiveness of the proposed scheme

    Numerical investigations of traveling singular sources problems via moving mesh method

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    This paper studies the numerical solution of traveling singular sources problems. In such problems, a big challenge is the sources move with different speeds, which are described by some ordinary differential equations. A predictor-corrector algorithm is presented to simulate the position of singular sources. Then a moving mesh method in conjunction with domain decomposition is derived for the underlying PDE. According to the positions of the sources, the whole domain is splitted into several subdomains, where moving mesh equations are solved respectively. On the resulting mesh, the computation of jump [uΛ™][\dot{u}] is avoided and the discretization of the underlying PDE is reduced into only two cases. In addition, the new method has a desired second-order of the spatial convergence. Numerical examples are presented to illustrate the convergence rates and the efficiency of the method. Blow-up phenomenon is also investigated for various motions of the sources

    Dynamics of entropic measurement-induced nonlocality in structured reservoirs

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    We propose the entropic measurement-induced nonlocality (MIN) as the maximal increment of von Neumann entropy induced by the locally non-disturbing measurement, and study behaviors of it both in the independent and common structured reservoirs. We present schemes for preserving the MIN, and show that for certain initial states the MIN, including the quantum correlations, can even be enhanced by the common reservoir. Additionally, we also show that the different measures of MIN may give different qualitative characterizations of nonlocal properties, i.e., it is rather measure dependent than state dependent.Comment: 8 pages, 6 figure

    Sudden change of geometric quantum discord in finite temperature reservoirs

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    We investigate sudden change (SC) behaviors of the distance-based measures of geometric quantum discords (GQDs) for two non-interacting qubits subject to the two-sided and the one-sided thermal reservoirs. We found that the GQDs defined by different distances exhibit different SCs, and thus the SCs are the combined result of the chosen discord measure and the property of a state. We also found that the thermal reservoir may generate states having different orderings related to different GQDs. These inherent differences of the GQDs reveal that they are incompatible in characterizing quantum correlations both quantitatively and qualitatively.Comment: 6 pages, 3 figures, the final version as that published in Annals of Physic
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