本文選題：量子糾纏 + 可分性判定準(zhǔn)則��； 參考：《電子科技大學(xué)》2016年博士論文

【摘要】：在科技不斷的發(fā)展過程中,物理學(xué)尤其是量子物理越來越和計(jì)算機(jī)科學(xué)、信息科學(xué)等學(xué)科緊密的聯(lián)系在了一起,隨之產(chǎn)生了量子信息學(xué)。而在量子信息學(xué)中,量子糾纏現(xiàn)象是一種獨(dú)特的資源,在量子信息學(xué)的絕大多數(shù)應(yīng)用中起著十分關(guān)鍵的作用。近幾十年來,量子糾纏吸引了越來越多的關(guān)注,人們?yōu)樯钊肜斫饧m纏現(xiàn)象付出了巨大的精力,并努力使之在實(shí)際應(yīng)用中發(fā)揮重要作用。例如,運(yùn)用糾纏可以將通信安全提升到一個(gè)新的高度。而量子計(jì)算將計(jì)算的概念煥然一新,以此為基礎(chǔ)的量子計(jì)算機(jī)更將會(huì)極大的改變計(jì)算機(jī)科學(xué)。毫無疑問,量子糾纏這一令人矚目的研究將會(huì)極大的推動(dòng)科技和社會(huì)的不斷進(jìn)步。論文以量子信息論和量子力學(xué)為背景,重點(diǎn)研究了糾纏的判定(或檢測(cè))和量化問題。給定一個(gè)量子態(tài)(狀態(tài)),如何判斷它是否是糾纏態(tài),或是可分態(tài)?這就需要用到可分性判定準(zhǔn)則(也稱為糾纏判據(jù))。當(dāng)前,已存在很多可分性判定準(zhǔn)則。但是直到現(xiàn)在,還沒有一個(gè)通用的判定方法,每一種方法都有特定的適用場(chǎng)合和局限性。如果已知一些量子態(tài)是糾纏的,我們是否可以去量化它們所含有“糾纏”的多少,以來比較哪個(gè)狀態(tài)含有的“糾纏”多。因?yàn)楹小凹m纏”多的狀態(tài)在實(shí)際應(yīng)用中可能效用更大或是更可靠,而“糾纏度(量)”這一概念就可以作為含有糾纏多少的定量描述。如今,大量的糾纏度定義被提出,它們分別有著不同的用途和考察角度,但是它們當(dāng)中大多難以計(jì)算。綜上,本論文就是旨在提出新的即容易理解、又方便計(jì)算的可分性準(zhǔn)則和糾纏度。主要?jiǎng)?chuàng)新如下:1.提出了基于量子態(tài)密度矩陣的秩的可分性判定準(zhǔn)則,該準(zhǔn)則可適用于任意多體系統(tǒng)純態(tài)。證明了一個(gè)多體量子態(tài)的(約化)密度矩陣的秩與糾纏有著密切的關(guān)系,它可以用來檢測(cè)糾纏是否存在。通過考察一個(gè)9)-qudit純態(tài)|?的29)-1-1個(gè)獨(dú)立的密度矩陣的秩,就可以判定該狀態(tài)是部分可分的、全可分的、或是一個(gè)真正的9)-qudit糾纏態(tài)。該方法對(duì)于糾纏的檢測(cè)是一個(gè)充分必要條件。2.提出了基于量子態(tài)系數(shù)矩陣的秩的可分性判定準(zhǔn)則。該準(zhǔn)則經(jīng)證明也是一個(gè)檢測(cè)糾纏的充分必要條件,并且與基于密度矩陣的秩的方法是等價(jià)的。兩種方法都便于理解和計(jì)算,還可以幫助我們找到任意一個(gè)多體純態(tài)的具體可分形式。3.基于量子態(tài)的系數(shù)矩陣,本文提出一個(gè)新的糾纏度。把系數(shù)矩陣的行列看作向量,該糾纏度定義只需要計(jì)算其向量長度及向量之間的角度。通過與著名的糾纏度定義concurrence作對(duì)比,驗(yàn)證了本文提出的方法是行之有效的,并且經(jīng)證明它滿足一個(gè)任意糾纏度定義都必須滿足的一些條件。該糾纏度計(jì)算簡單,且具有清楚的幾何意義。4.基于量子態(tài)的(約化)密度矩陣,本文還提出一個(gè)新的適用于任意9)-qudit態(tài)的多體糾纏度。經(jīng)證明,它也是一個(gè)有效的糾纏度定義,該方法能夠分辨出相對(duì)高度糾纏和最大糾纏。以上所提出的方法都經(jīng)過了具體計(jì)算實(shí)例的對(duì)比驗(yàn)證,它表明我們所提出的方法易于理解,計(jì)算簡單,具有良好的適用性。
[Abstract]:In the course of the continuous development of science and technology, physics, especially quantum physics, has become more and more closely linked with computer science, information science and other disciplines, resulting in quantum informatics. In quantum informatics, quantum entanglement is a unique resource and plays a very important role in the vast majority of applications of quantum information. In recent decades, quantum entanglement has attracted more and more attention. People have made great efforts to understand entanglement in depth and try to play an important role in practical applications. For example, the use of entanglement can raise the security of communication to a new high degree. The quantum computer will greatly change the computer science. There is no doubt that quantum entanglement, a remarkable research, will greatly promote the continuous progress of science and technology and society. The thesis focuses on the determination (or detection) and quantization of entanglement in the context of quantum information and quantum mechanics. State (state), how to judge whether it is an entangled state or a separable state? This requires the use of separability criteria (also known as entanglement criteria). At present, there are many separability criteria. But until now, there is no general determination method, each method has a specific application and limitations. If some of the methods are known, some of them are known. The quantum state is entangled. Whether we can quantify the number of entanglement they contain and which states have more entanglement. Because the state of "entanglement" may be more effective or more reliable in practical applications, the concept of "entanglement" can be used as an entanglement. A large number of definitions of entanglement have been proposed, and they have different uses and angles of investigation, but most of them are difficult to calculate. To sum up, this paper is aimed at proposing a new separability criterion and entanglement degree which is easy to understand and convenient to calculate. The main innovations are as follows: 1. the quantum density matrix based on the quantum state matrix is proposed. The criterion for determining the separability of a rank, which can be applied to the pure state of any multibody system. It is proved that the rank of a (Reductive) density matrix of a multibody state is closely related to the entanglement. It can be used to detect the existence of entanglement. By examining the rank of the -1-1 independent density matrix of a 9) -qudit pure state? It can be judged by the rank of the independent density matrix. The state is partially separable, all separable, or a real 9 -qudit entanglement state. This method is a sufficient and necessary condition for the detection of entanglement..2. proposes the criterion of separability based on the rank of the quantum state coefficient matrix. The criterion is proved to be a sufficient and necessary condition for detecting entanglement and is also a density matrix based on the density matrix. The rank method is equivalent. The two methods are easy to understand and calculate. We can also help us find the coefficient matrix of the specific separable form of a multibody pure state.3. based on the quantum state. In this paper, we propose a new degree of entanglement. The ranks of the coefficients matrix are regarded as a vector. The definition of the degree of entanglement only needs to calculate the length and vector of the vector. By comparing with the famous entanglement definition concurrence, it is proved that the method proposed in this paper is effective and proves that it satisfies some conditions that the definition of any entanglement degree must be satisfied. The entanglement is simple and has a clear geometric meaning.4. based on the quantum state (reduced) density matrix. This paper also proposes a new multibody entanglement degree for any 9 -qudit state. It is proved that it is also an effective definition of entanglement. The method can distinguish relative high entanglement and maximum entanglement. The proposed method has been verified by the comparison of concrete examples. It shows that the method we proposed is easy to understand and calculate. It is simple and has good applicability.
【學(xué)位授予單位】：電子科技大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2016
【分類號(hào)】：O413

【參考文獻(xiàn)】

相關(guān)博士學(xué)位論文 前1條

1 張國鋒;量子糾纏的若干問題研究[D];山西大學(xué);2004年

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本文編號(hào)：2056058