刻画Banach空间闭单位球上的保凸双射与量子关联消失的信道

发布时间：2018-06-16 15:43

  本文选题：Banach空间 + 量子信道　； 参考：《太原理工大学》2017年硕士论文

【摘要】：算子代数上的保持问题是研究用尽可能少的同构不变量来刻画算子代数之间的映射,这一课题已有百年的研究历史,一直是算子理论与算子代数研究的重要分支之一.近年来,这一领域越来越多的研究成果被应用于量子信息理论中,帮助描述和解决量子信息理论中的基本概念和问题.例如,量子信道就是密度算子上保迹的完全正映射,量子门就是Hilbert空间上的酉变换.本文研究Banach空间闭单位球上的双边保凸双射与量子关联消失信道的刻画问题.主要获得了以下结果:1.设X是一个严格凸的实Banach空间且dim X2,B1(X)是X的闭单位球.对于双射φ:B1(X)→B1(X),下列条件等价:(a)φ是仿射;(b)φ双边保凸组合,即,φ([x,y])=[φ(x),φ(y)],x,y ∈ B1(X);(c)φ对任意的x ∈B1(H),满足x → Ux,其中U是X上的一个可逆有界线性等距算子.2.设Φ是一个有限维系统上的量子信道,则下列等价:(a)存在一族满足∑Wi=I的正算子Wi,以及就范正交基ei,使得Φ(ρ)= ∑tr(Wiρ)|ei)(ei|;(b)Φ是局部A-失谐消失信道;(c)Φ(?)Id将极大纠缠态映为CQ态(即经典(classical)-量子(quantum)态).
[Abstract]:The maintenance problem on operator algebra is to study the mapping between operator algebras with as few isomorphism invariants as possible. This subject has been studied for a hundred years and has been one of the important branches of operator theory and operator algebra research. In recent years, more and more research results in this field have been applied to quantum information theory, helping to describe and solve the basic concepts and problems in quantum information theory. For example, the quantum channel is a completely positive mapping preserving trace on the density operator, and the quantum gate is the unitary transformation on Hilbert space. In this paper, we study the characterization of two-sided convex preserving bijection and quantum correlated vanishing channels on closed unit spheres in Banach spaces. The main results are as follows: 1. Let X be a strictly convex real Banach space and dim X _ 2n B _ 1 X) be a closed unit ball of X. For a bijective 蠁: B1 / X) B1 / X1, the following conditions are equivalent to 1: a) 蠁 is an affine convexity preserving combination, that is, 蠁 ([xy] n = [蠁 X, 蠁 y]) 蠁 for any x 鈭，

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