發(fā)布時(shí)間：2018-01-05 07:14

  本文關(guān)鍵詞：Ket-Bra糾纏態(tài)方法及其在開(kāi)放量子系統(tǒng)中的應(yīng)用　出處：《中國(guó)科學(xué)技術(shù)大學(xué)》2016年博士論文　論文類型：學(xué)位論文

  更多相關(guān)文章： Ket-Bra糾纏態(tài)方法 開(kāi)放量子系統(tǒng) 量子退相干 糾纏演化 開(kāi)放自旋鏈

【摘要】：在上世紀(jì)末量子力學(xué)與信息技術(shù)、計(jì)算科學(xué)的結(jié)合催生了一門全新的交叉學(xué)科——量子信息,甫一出世量子信息便由于其潛在的應(yīng)用價(jià)值和物理前景吸引了物理學(xué)界的注意力;量子相干與量子糾纏作為一種重要資源在量子通信、量子調(diào)控和量子計(jì)算等領(lǐng)域有著舉足輕重的地位,這是因?yàn)橄到y(tǒng)的相干性和糾纏性是實(shí)現(xiàn)量子并行算法和量子通信的基礎(chǔ)。然而,真實(shí)的量子系統(tǒng)總是會(huì)隨著時(shí)間的演化逐漸丟失其相干性和糾纏性最終導(dǎo)致系統(tǒng)退化到徹底的混態(tài)或可分離態(tài),此外這種演化過(guò)程一般是非幺正的不可逆的,因此這種過(guò)程是量子計(jì)算和量子通信實(shí)用化的最大障礙。理論上講,孤立封閉的量子系統(tǒng)遵循幺正演化,然而不可能有量子系統(tǒng)與外界徹底隔絕,系統(tǒng)與外界環(huán)境間總存在著各種相互作用,因此其在演化過(guò)程中不可避免的受到來(lái)自外界周圍環(huán)境的影響；這種來(lái)自外界的影響將導(dǎo)致量子系統(tǒng)的非幺正演化,使系統(tǒng)逐漸丟失其相干性、糾纏性等量子特性蛻化為經(jīng)典的混態(tài)；而量子信息、量子計(jì)算在很大程度上依賴量子操作的幺正性,正是退相干這一原因極大的阻礙了量子通信和量子計(jì)算的進(jìn)步。為了真正實(shí)現(xiàn)量子通信和量子計(jì)算等技術(shù),人們對(duì)開(kāi)放量子系統(tǒng)開(kāi)展了全面而深入的研究；一般而言開(kāi)放量子系統(tǒng)將整個(gè)體系分為系統(tǒng)和環(huán)境兩部分,而后從體系的整個(gè)哈密頓量出發(fā)利用海森堡方程給出整個(gè)體系的演化方程,最后利用Born-Markov近似并對(duì)方程兩端環(huán)境部分求偏跡即可得到關(guān)于系統(tǒng)部分的約化密度算符主方程。主方程從數(shù)學(xué)形式看是一種復(fù)雜的算符方程,為了求解主方程人們發(fā)展出了若干種方法,主要可以分為C-數(shù)方法和超算符(Super-Operator Method)方法兩大類,然而無(wú)論C-數(shù)方法還是超算符方法都有著難以克服的缺點(diǎn),例如C-數(shù)方法將主方程轉(zhuǎn)化為F-P方程后求解困難、繁瑣且其解并不適用于任意初態(tài),超算符方法則依賴于主方程本身的的Lie代數(shù)結(jié)構(gòu),因此若主方程不具有Lie代數(shù)結(jié)構(gòu)則超算符方法不再適用,這一缺點(diǎn)大大限制了超算符方法的應(yīng)用范圍。綜上所述,我們選擇了主方程的求解作為研究開(kāi)放量子系統(tǒng)的切入點(diǎn),經(jīng)過(guò)大量的推導(dǎo)計(jì)算后,我們提出了新的Ket-Bra糾纏態(tài)方法(Ket-Bra Entangled Stste KBES Method)用于求解主方程；Ket-Bra糾纏態(tài)方法能夠?qū)⒅鞣匠剔D(zhuǎn)化為類薛定諤方程(Schrodinger-like Equation)并求解,與C-數(shù)方法和超算符方法相比,Ket-Bra糾纏態(tài)方法有如下優(yōu)點(diǎn)：1. Ket-Bra糾纏態(tài)方法方法應(yīng)用范圍廣,理論上能求解任意有限維能級(jí)系統(tǒng)的主方程；而超算符方法則依賴主方程的Lie代數(shù)結(jié)構(gòu),即使主方程的細(xì)微改變即可導(dǎo)致超算符方法不再適用。2. Ket-Bra糾纏態(tài)方法求解過(guò)程簡(jiǎn)單方便、物理意義清晰明了其解適用于任意初態(tài),且主要計(jì)算可以通過(guò)計(jì)算機(jī)完成：3. Ket-Bra糾纏態(tài)方法能夠?qū)⒅鞣匠剔D(zhuǎn)化為薛定諤方程,這使得求解薛定諤方程的成熟方法同樣可用于求解主方程,例如演化算符法、定態(tài)方法、微擾法、不變算符法等方法都可通過(guò)Ket-Bra糾纏態(tài)方法求解主方程,尤其定態(tài)方法更能直接給出主方程的最終穩(wěn)定態(tài)。隨后我們利用此Ket-Bra糾纏態(tài)方法求解了若干開(kāi)放量子系統(tǒng)的主方程,包括含時(shí)外場(chǎng)中的二能級(jí)原子的耗散主方程、三能級(jí)的V型原子耗散主方程、2-Qubit XYZ型開(kāi)放自旋鏈的主方程、N-Qubit XXZ型開(kāi)放自旋鏈主方程等,并對(duì)這些系統(tǒng)的退相干過(guò)程和退糾纏過(guò)程進(jìn)行了研究,研究結(jié)果顯示系統(tǒng)內(nèi)部的相互作用會(huì)導(dǎo)致其在糾纏演化過(guò)程中出現(xiàn)糾纏死亡(Entanglement Sudden Death簡(jiǎn)稱ESD)和糾纏復(fù)活(Entanglement Sudden Birth簡(jiǎn)稱ESB)現(xiàn)象,且這種來(lái)自系統(tǒng)內(nèi)部的子系統(tǒng)間的相互作用能在一定程度上抑制系統(tǒng)的退相干和退糾纏過(guò)程,尤其對(duì)2-Qubit XYZ型開(kāi)放自旋鏈的研究更顯示即使在t→∞時(shí),系統(tǒng)仍能保持一定的糾纏。對(duì)含時(shí)外場(chǎng)中二能級(jí)原子研究發(fā)現(xiàn),即使在馬爾科夫近似下且系統(tǒng)內(nèi)部不存在任何相互作用,通過(guò)對(duì)系統(tǒng)施加含時(shí)外場(chǎng)仍然可以使系統(tǒng)出現(xiàn)糾纏復(fù)活現(xiàn)象；這些研究表明通過(guò)系統(tǒng)內(nèi)部的相互作用或?qū)ο到y(tǒng)施加外場(chǎng)來(lái)抑制退相干的方案在理論上具有一定的可行性,有助于人們?cè)谕讼喔蓡?wèn)題的研究上取得更大突破。
[Abstract]:At the end of the last century of quantum mechanics and information technology, computing science with spawned a new interdisciplinary field of quantum information, quantum information will be born soon because of its potential application value and prospect in the field of physics, physics has attracted attention; quantum coherence and quantum entanglement is an important resource in quantum communication, quantum control and quantum computing has a pivotal position, this is because the system is the realization of coherence and entanglement of quantum parallel algorithm and quantum communication. However, the quantum system real time evolution will always be with the gradual loss of the coherence and entanglement eventually lead to system degradation to a complete separable or mixed state in addition to this state, the evolution process is generally non unitary and irreversible, so this process is the biggest obstacle in quantum computation and quantum communication practice. Theoretically, solitary Vertical closed quantum system follow the unitary evolution, however, may not be completely cut off from the quantum system with the outside world, between the system and environment there is always a variety of interactions, so it is inevitable in the process of evolution is influenced by the surrounding environment; the influence from outside will lead to non unitary evolution of quantum system the system, gradually lost its coherence, entanglement and quantum properties of degenerate mixed states of classical and quantum information, quantum computation; quantum operation dependent largely on the unitarity, it is decoherence for this reason greatly hindered the progress of quantum communication and quantum computation. In order to realize quantum communication and quantum computing technology, people on the open quantum system to carry out a comprehensive and in-depth research; general open quantum system the whole system is divided into two parts of the system and the environment, and then from the The Hamiltonian of the evolution equation of Heisenberg equation of the system, finally using the Born-Markov approximation and some equations can be obtained at both ends of the environment and partial trace reduced density operator equations of the system. The main part of the master equation from mathematical form is a kind of complex operator equation, in order to solve the main equation of people developed several methods can be divided into C- number method and super operator (Super-Operator Method) method in two categories, however the number of C- method or super operator method is difficult to overcome the shortcomings, such as the C- number method of the master equation is transformed into F-P equation after the solution is difficult, tedious and the solution is not applicable to arbitrary initial states. Lie super operator method of algebraic structure depends on the master equation itself, so if the master equation has no Lie algebra structure super operator method is no longer applicable, the disadvantage of large. The scope of application for super operator method. To sum up, we chose the solving master equation as a starting point of open quantum system, after a lot of calculation, we propose a new method of entangled Ket-Bra (Ket-Bra Entangled Stste KBES Method) is used to solve the master equation; Ket-Bra entangled state can be transformed into the master equation for the Schrodinger equation (Schrodinger-like Equation) and is compared with the C- method and the super operator method, entangled Ket-Bra method has the following advantages: 1. Ket-Bra entangled state method method of wide application range, the main equations in any finite dimensional level system theory; Lie algebra structure and super operator method is dependent on the main equation and even if the main equations can lead to subtle changes in the super operator method is no longer suitable for.2. Ket-Bra entangled state method is simple and convenient, the physical meaning is clear The solution is applicable to arbitrary initial states, and the main calculation can be finished by computer: 3. Ket-Bra entangled state can be transformed into the master equation of the Schrodinger equation, which makes the mature method for solving Schrodinger equation can also be used for solving the master equation, such as evolution operator method, steady state method, perturbation method, invariant operator method etc. methods by Ket-Bra entangled state method solving the master equation, especially the steady state method can directly give the final steady state master equation. Then we use the Ket-Bra method to solve the master equation of entanglement of several open quantum systems, including two level atom field in dissipative V type atomic master equation, the main dissipation equation of three-level, 2-Qubit master equation of open type XYZ spin chain, N-Qubit XXZ open spin chain master equation, and the system decoherence and disentanglement process research, research The results show that the interaction of the system will lead to the death of entanglement in the entanglement evolution process (Entanglement Sudden Death ESD (Entanglement Sudden) and entanglement resurrection Birth referred to as ESB), and the interaction of subsystems from the internal system between can inhibit the system to a certain extent the decoherence and disentanglement process. Especially study the spin chain of 2-Qubit open type XYZ also showed that even in the T approaches infinity, the system can still maintain a certain degree of entanglement. With two level atoms in the field study found that even in the Markoff approximation and the system does not exist any interaction, by applying the time-dependent external field can still make the system have the entanglement resurrection the phenomenon of the system; these studies show that the interaction within the system or the system to suppress the decoherence of the external solution has some in theory The feasibility is helpful for people to make greater breakthroughs in the research of the problem of decoherence.

【學(xué)位授予單位】：中國(guó)科學(xué)技術(shù)大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2016
【分類號(hào)】：O413

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