Viện Toán học Và Khoa học Ứng dụng Thăng Long

Secure communication in general and secure dialogue in particular are highly demanded, especially in the current information exploding era. Here we are concerned with secure dialogue. Because any dialogue conducted merely by classical means is fully eavesdropped without traces left behind, quantum version of dialogue, the so-called quantum dialogue, offers a promising solution to the security problem. The security desired does not simply focus on the exchanged information but also on their classical correlations, i.e., a quantum dialogue protocol should be protected from both information theft and information leakage. Such a secure quantum dialogue protocol is proposed in this paper employing Greenberger-Horne-Zeilinger states as the quantum channel. The above-mentioned requirement for security is achieved in message rounds by using extra random bits for the encoding/decoding processes combined with two kinds of control rounds which are designed to detect eavesdropping, if any.  

Fritz John necessary conditions for local Henig and global efficient solutions of vector equilibrium problems involving equality, inequality and set constraints with nonsmooth functions are established via convexificators. Under suitable constraint qualications, Kuhn-Tucker necessary conditions for local Henig and gobally efficient solutions are derived. Note that Henig and global efficient solutions of (VEP) are studied with respect to a closed convex cone. Sufficient condition for Henig and globally efficient solutions are derived under some assumptions on asymptotic semiinvexityinfne of the problem. Some illustrative examples are also given.

Noise is unavoidable in practice and its presence makes quantum protocols imperfect. In this paper we consider a way to cope with typical types of noise in joint remote preparation of an arbitrary 2-qubit state. The idea is to use nonmaximally (in stead of maximally) entangled states as the initial quantum channel. Because noise changes the initial quantum channel we can beforehand tailor it to be nonmaximally entangled by introducing free parameters which, depending on given types of noise, can be controlled so that due to the affect of noise the initial quantum channel becomes closest to the maximally entangled one, thus optimizing the performance of the joint remote state preparation protocol. The dependence of the optimal averaged fidelities on the strength of various types of noise is represented by phase diagrams that clearly separate the quantum domain from the classical one.

We explain a new idea of how to use the high probability interval thresholds for neurons in quantum neural networks. Some basic quantum neural networks were analyzed and constructed in a recent work of the author. In particular the Least Square Error Problem (LSEP) and the Linear Regression Problem (LRP) was discussed. In this paper we an- alyze a new look on the threshold rules for neurons, taking the intervals of high probability in place of classical sigmoid half-line threshold and then we construct the least-square quantum neural network (LS-QNN), the poly- nomial interpolation quantum neural network (PI-QNN), the polynomial regression quantum neural network (PR-QNN) and chi-squared quantum neural network (X2-QNN). We use the corresponding solutions or statistical tests as the threshold for the corresponding training rules.