38,668 research outputs found

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

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

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 $a \ge 0$, $p>1$ and $\Omega \subset \mathbb{R}^n$ is
an unbounded domain of $\mathbb{R}^n$, $n \ge 5$. 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

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 $\Omega$ is a subset of $\mathbb{R}^N$, $N \ge 5$, $\alpha
>-4$, $0 \le \beta \le \dfrac{N-4}{2}$, $p>1$ and $\vartheta=1$. 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

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

Many machine learning problems can be reduced to learning a low-rank positive
semidefinite matrix (denoted as $Z$), 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 $Z$ $quadraticly$ as $XX^\top$. 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 $Z$
$bilinearly$ as $XY^\top$ and using a Courant penalty to penalize the
difference of $X$ and $Y$, 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
$L$-Lipschitz-smooth and $\sigma-$strongly convex, such that the proposed
surrogate will solve the original SDP when the penalty parameter is larger than
this bound, that is $\gamma>\frac{1}{4}(L-\sigma)$. 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

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

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

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
$[\dot{u}]$ 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

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

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

- â€¦