本文關(guān)鍵詞： 不確定性關(guān)系 斜信息 WYD斜信息 廣義度量調(diào)整斜信息 關(guān)聯(lián)測度 方差 協(xié)方差 協(xié)方差矩陣 馬爾科夫性 統(tǒng)一熵　出處：《陜西師范大學(xué)》2016年博士論文　論文類型：學(xué)位論文

【摘要】：本文利用算子理論與算子代數(shù)的知識研究了量子信息中的不確定性理論及其應(yīng)用.建立了廣義度量調(diào)整斜信息的不確定性關(guān)系;給出了非自伴算子對應(yīng)的Wigner-Yanase-Dyson(WYD)斜信息以及相關(guān)的一些物理量的定義,并建立了相關(guān)的不確定性關(guān)系;證明了關(guān)于混合態(tài)的方差的和式以及乘積式的不確定性關(guān)系;從不確定性理論的角度,利用協(xié)方差矩陣刻畫了非馬爾科夫性;證明了統(tǒng)一熵關(guān)于參數(shù)的單調(diào)性以及凹凸性.本文共分五章,主要內(nèi)容如下:第一章介紹了本文的研究背景及現(xiàn)狀,并列出了本文要用到的符號,定義以及相關(guān)已有成果.第二章引入了量化關(guān)聯(lián)的度量函數(shù)Fa,α(ρab),得到了如下結(jié)論:對于經(jīng)典-量子態(tài)Pab,Fa,α(Pab)= 0當(dāng)且僅當(dāng)ρab是乘積態(tài);Fa,α(ρab)是局部酉不變的且在具有相同的邊際態(tài)ρa之集上是凸的;Fa,α(ρab)在B(Hb)上的局部隨機酉運算作用下是不增的;對于一個量子-經(jīng)典態(tài)ρab,Fa,α(ρab)在B(Hb)上的局部量子運算作用下是不增的;最后,我們分別計算了純態(tài)以及Bell-對角態(tài)的關(guān)聯(lián)度量Fa,α(ρab).第三章建立了關(guān)于廣義度量調(diào)整斜信息以及廣義度量調(diào)整關(guān)聯(lián)測度的不確定性關(guān)系,并由此利用幾種典型的算子單調(diào)函數(shù)得到一些關(guān)于斜信息和WYD斜信息的不確定性關(guān)系.引入了非自伴算子對應(yīng)的廣義WYD關(guān)聯(lián)測度,廣義WYD斜信息以及一些相關(guān)的物理量,討論了它們的性質(zhì),建立了關(guān)于廣義WYD斜信息的一些不確定性關(guān)系.此外,給出了兩個可觀測量關(guān)于混合態(tài)的方差的和的下界,保證了當(dāng)兩個可觀測量在系統(tǒng)態(tài)上是不相容時,結(jié)果是不平凡的.我們還建立了關(guān)于兩個可觀測量方差的乘積的更強的不確定性關(guān)系.同時,我們得到三個可觀測量關(guān)于混合態(tài)的幾種強不確定性關(guān)系.第四章提出了量子演化的非馬爾科夫性的新刻畫,從不確定性角度利用協(xié)方差矩陣來刻畫非馬爾科夫性,得到了關(guān)于協(xié)方差矩陣的基本性質(zhì).考慮了幾種典型的例子,并將我們的度量與Fisher信息矩陣刻畫,可除性刻畫以及Breuer-Laine-Piilo(BLP)刻畫進行了比較研究.第五章刻畫了統(tǒng)一量子(r,s)-熵關(guān)于參數(shù)的單調(diào)性以及凹凸性,主要結(jié)論如下:(ⅰ)對于任意給定的0rl,Ers(ρ)關(guān)于s ∈(-∞,+∞)是單調(diào)增加的,以及對于任意的r ≥ 1,Ers(ρ)關(guān)于s ∈(-∞,+∞)是單調(diào)減少的;(ⅱ)對于任意的s0,Ers(ρ)關(guān)于r ∈(0,+∞)是單調(diào)減少的;(ⅲ)對于乘積態(tài)ρab,存在實數(shù)a和b使得當(dāng)r ≥ 1時,Irs(ρab)關(guān)于∈[0,a]是單調(diào)增加的,以及當(dāng)0r1時,它關(guān)于s ∈[b,0]是單調(diào)減少的;(ⅳ)對于乘積態(tài)ρab,m2且m-21nm = 1,對于每一個 s0,Irs(ρab)關(guān)于 r ∈[rs,+∞)是減少的,其中 = max{as,bs},且a,ss滿足trρaas= trρbbs=m =-1/s(ⅴ)對于任意的r0,Ers(ρ)關(guān)于s∈(-∞,+∞)是凸函數(shù).
[Abstract]:In this paper, the uncertainty theory and its application in quantum information are studied by means of operator theory and operator algebra, and the uncertainty relation of generalized metric adjusted skew information is established. In this paper, the skew information of Wigner-Yanase-Dysonn WYDcorresponding to non-self-adjoint operators and the definition of some related physical quantities are given, and the related uncertainty relations are established. The sum of variances of mixed states and the uncertain relation of product are proved. The non-Markov property is characterized by covariance matrix from the perspective of uncertainty theory. This paper is divided into five chapters. The main contents are as follows: the first chapter introduces the research background and current situation of this paper, and lists the symbols to be used in this paper. In chapter 2, we introduce the quantized correlation metric function Fa, 偽 (蟻 abg), and obtain the following conclusion: for the classical quantum state Paban Fa. A Pabu = 0 if and only if 蟻 ab is a product state; Fa, 偽 (蟻 ab) is locally unitary invariant and convex on the set with the same marginal state 蟻 a; Faa, 偽 (蟻 ab) is not increased under the action of local random unitary operation on BHb. For a quantum-classical state 蟻 abn Faa, 偽 (蟻 abs) is not increased under the action of local quantum operations on BHb. Finally, we calculate the correlation metric Fa of pure states and Bell-diagonal states, respectively. In Chapter 3, the uncertainty relation of generalized metric adjusted skew information and generalized metric adjusted correlation measure is established. By using some typical operator monotone functions, some uncertain relations about skew information and WYD skew information are obtained, and the generalized WYD correlation measure corresponding to non-self-adjoint operators is introduced. The properties of generalized WYD oblique information and some related physical quantities are discussed, and some uncertain relations about generalized WYD oblique information are established. The lower bound of the sum of variance of two observable measurements for mixed states is given, which ensures that the two observable measurements are incompatible in the system state. The result is not trivial. We also establish a stronger uncertainty relation about the product of two observable measurements of variance. We obtain three strong uncertainty relations of observable measurements on mixed states. Chapter 4th presents a new characterization of non-Markov properties of quantum evolution. In this paper, we use the covariance matrix to characterize the non-Markov property from the uncertainty point of view, and obtain the basic properties of the covariance matrix. Some typical examples are considered. And we depict our metrics and Fisher information matrix. The divisibility characterization and Breuer-Laine-Piilo BLP characterization are compared. Chapter 5th characterizes the unified quantum r. For the monotonicity and concave convexity of parameters, the main conclusions are as follows: (I) is monotone increasing for any given 0 rln Ers (蟻) in relation to s 鈭，

本文編號：1446674