本文選題：Banach空間 + 量子信道��； 參考：《太原理工大學(xué)》2017年碩士論文

【摘要】：算子代數(shù)上的保持問題是研究用盡可能少的同構(gòu)不變量來刻畫算子代數(shù)之間的映射,這一課題已有百年的研究歷史,一直是算子理論與算子代數(shù)研究的重要分支之一.近年來,這一領(lǐng)域越來越多的研究成果被應(yīng)用于量子信息理論中,幫助描述和解決量子信息理論中的基本概念和問題.例如,量子信道就是密度算子上保跡的完全正映射,量子門就是Hilbert空間上的酉變換.本文研究Banach空間閉單位球上的雙邊保凸雙射與量子關(guān)聯(lián)消失信道的刻畫問題.主要獲得了以下結(jié)果:1.設(shè)X是一個(gè)嚴(yán)格凸的實(shí)Banach空間且dim X2,B1(X)是X的閉單位球.對(duì)于雙射φ:B1(X)→B1(X),下列條件等價(jià):(a)φ是仿射;(b)φ雙邊保凸組合,即,φ([x,y])=[φ(x),φ(y)],x,y ∈ B1(X);(c)φ對(duì)任意的x ∈B1(H),滿足x → Ux,其中U是X上的一個(gè)可逆有界線性等距算子.2.設(shè)Φ是一個(gè)有限維系統(tǒng)上的量子信道,則下列等價(jià):(a)存在一族滿足∑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-失諧消失信道;(c)Φ(?)Id將極大糾纏態(tài)映為CQ態(tài)(即經(jīng)典(classical)-量子(quantum)態(tài)).
[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，

本文編號(hào)：2027208