Probabilistic teleportation of an arbitrary three-particle state

A scheme for teleporting an arbitrary and unknown three-particle state from a sender to either one of two receivers is proposed. The quantum channel is composed of a two-particle non-maximally entangled state and two three-particle non-maximally entangled W states. An arbitrary three-particle state can be perfectly teleported probabilistically if the sender performs three generalized Bell-state measurements and sends to the two receivers the classical result of these measurements, and either one of the two receivers adopts an appropriate unitary transformation conditioned on the suitable measurement outcomes of the other receiver. All kinds of unitary transformations are given in detail.     

关于一个矩阵迹的不等式的注记

本文修正了［２］中的一个矩阵迹的不等式的一些错误，证明了ｔｒ［（Ａａ一Ｂａ）（Ａ一β一Ｂβ）］＜０当且仅当αβ＞０且Ａ≠Ｂ，ｔｒ［（Ａａ－Ｂａ）（Ａ－β－Ｂ－β）］＞０当且仅当αβ＜０且Ａ≠Ｂ，这里Ａ，Ｂ是ｎ×ｎ的Ｈｅｒｍｉｔｅ正定矩阵．     

与不变量有关的幺正变换方法和三次量子化宇宙波函数的演化

首先在推广了的量子不变量理论的基础上建立了与不变量有关的立正变换方法,并用此方法研究了三次量子化宇宙波函数的演化,求得了系统的相因子、波函数.并通过构造相干态求得了Wheeler—Dewitt方程的解以及由三次量子化引起的相对量子起伏.     

Moment problem with contractive solutions: the regular case

An operator multivariate moment problem with contractive solutions having regular unitary dilation is characterized in terms of the initial data. This extends a recent result of Sebestyén and Popovici, but the ideas of our proof differ from those used by them. The connection between the operator multivariate moment problem and harmonizable multivariate discrete processes is mentioned.

     

C^＊-代数中的等价

在算子理论和算子代数的研究中，等价是一个很重要的工具，它对K-理论的研究和理解起着很重要的作用．寻找等价关系是研究不变量的一种方法，为了使大家更好的认识和学习C^＊-代数，我们在本文研究了算子代数中经常用到的代数等价、酉等价、同伦等几种等价之间的关系．     

Generalizations of P. Lévy's inversion theorem

We extend the Lévy inversion formula for the recovery of a bounded measure over $\text{R}$ from its Fourier-Stieltjes transform to bounded complex-valued, orthogonally scattered Hilbert space-valued, and spectral projection operator-valued measures over any first countable locally compact Abelian group. All our results are direct generalizations of known inversions for $\text{R}$.     

Single particle SU(3) parentage coefficients

The single particle SU(3) parentage coefficients are calculated for the case of leading SU(3) representation in the highest orbital symmetry partition, using the method suggested by Hecht. Tabulations are given for all possible cases of identical nucleons in η=3 and η=4 shells.     

Integral Formulas for the Minimal Representation of O(p,2)

The minimal representation of O(p,q) (p+q: even) is realized on the Hilbert space of square integrable functions on the conical subvariety of R^p+q–2. This model presents a close resemblance of the Schrödinger model of the Segal–Shale–Weil representation of the metaplectic group. We shall give explicit integral formulas for the inversion together with the analytic continuation to a certain semigroup of O(p+2,C) of the minimal representation of O(p,2) by using Bessel functions.Mathematics Subject Classifications (2000) primary 22E30; secondary 22E46, 20M20, 43A80.     

Maxima of entries of Haar distributed matrices

Let _n=(_ij) be an n×n random matrix such that its distribution is the normalized Haar measure on the orthogonal group O(n). Let also W_n:=max_1i,jn|_ij|. We obtain the limiting distribution and a strong limit theorem on W_n. A tool has been developed to prove these results. It says that up to n/( log n)² columns of _n can be approximated simultaneously by those of some Y_n=(y_ij) in which y_ij are independent standard normals. Similar results are derived also for the unitary group U(n), the special orthogonal group SO(n), and the special unitary group SU(n).Mathematics Subject Classification (2000):15A52, 60B10, 60B15, 60F10