Multiparty Quantum Secret Sharing

Based on a quantum secure direct communication (QSDC) protocol [Phys. Rev. A69(04)052319], we propose a $(n,n)$-threshold scheme of multiparty quantum secret sharing of classical messages (QSSCM) using only single photons. We take advantage of this multiparty QSSCM scheme to establish a scheme of multiparty secret sharing of quantum information (SSQI), in which only all quantum information receivers collaborate can the original qubit be reconstructed. A general idea is also proposed for constructing multiparty SSQI schemes from any QSSCM scheme

Equation of motion for multiqubit entanglement in multiple independent noisy channels

We investigate the possibility and conditions to factorize the entanglement evolution of a multiqubit system passing through multi-sided noisy channels. By means of a lower bound of concurrence (LBC) as entanglement measure, we derive an explicit formula of LBC evolution of the N-qubit generalized Greenberger-Horne-Zeilinger (GGHZ) state under some typical noisy channels, based on which two kinds of factorizing conditions for the LBC evolution are presented. In this case, the time-dependent LBC can be determined by a product of initial LBC of the system and the LBC evolution of a maximally entangled GGHZ state under the same multi-sided noisy channels. We analyze the realistic situations where these two kinds of factorizing conditions can be satisfied. In addition, we also discuss the dependence of entanglement robustness on the number of the qubits and that of the noisy channels.Comment: 14 page

ReSync: Riemannian Subgradient-based Robust Rotation Synchronization

This work presents ReSync, a Riemannian subgradient-based algorithm for solving the robust rotation synchronization problem, which arises in various engineering applications. ReSync solves a least-unsquared minimization formulation over the rotation group, which is nonsmooth and nonconvex, and aims at recovering the underlying rotations directly. We provide strong theoretical guarantees for ReSync under the random corruption setting. Specifically, we first show that the initialization procedure of ReSync yields a proper initial point that lies in a local region around the ground-truth rotations. We next establish the weak sharpness property of the aforementioned formulation and then utilize this property to derive the local linear convergence of ReSync to the ground-truth rotations. By combining these guarantees, we conclude that ReSync converges linearly to the ground-truth rotations under appropriate conditions. Experiment results demonstrate the effectiveness of ReSync.Comment: 24 pages, 3 figure

Pressure Transient Analysis of Dual Fractal Reservoir

A dual fractal reservoir transient flow model was created by embedding a fracture system simulated by a tree-shaped fractal network into a matrix system simulated by fractal porous media. The dimensionless bottom hole pressure model was created using the Laplace transform and Stehfest numerical inversion methods. According to the model's solution, the bilogarithmic type curves of the dual fractal reservoirs are illustrated, and the influence of different fractal factors on pressure transient responses is discussed. This semianalytical model provides a practical and reliable method for empirical applications