Ket-Bra纠缠态方法及其在开放量子系统中的应用

发布时间：2018-01-05 07:14

本文关键词：Ket-Bra纠缠态方法及其在开放量子系统中的应用　出处：《中国科学技术大学》2016年博士论文　论文类型：学位论文

【摘要】：在上世纪末量子力学与信息技术、计算科学的结合催生了一门全新的交叉学科——量子信息,甫一出世量子信息便由于其潜在的应用价值和物理前景吸引了物理学界的注意力;量子相干与量子纠缠作为一种重要资源在量子通信、量子调控和量子计算等领域有着举足轻重的地位,这是因为系统的相干性和纠缠性是实现量子并行算法和量子通信的基础。然而,真实的量子系统总是会随着时间的演化逐渐丢失其相干性和纠缠性最终导致系统退化到彻底的混态或可分离态,此外这种演化过程一般是非幺正的不可逆的,因此这种过程是量子计算和量子通信实用化的最大障碍。理论上讲,孤立封闭的量子系统遵循幺正演化,然而不可能有量子系统与外界彻底隔绝,系统与外界环境间总存在着各种相互作用,因此其在演化过程中不可避免的受到来自外界周围环境的影响；这种来自外界的影响将导致量子系统的非幺正演化,使系统逐渐丢失其相干性、纠缠性等量子特性蜕化为经典的混态；而量子信息、量子计算在很大程度上依赖量子操作的幺正性,正是退相干这一原因极大的阻碍了量子通信和量子计算的进步。为了真正实现量子通信和量子计算等技术,人们对开放量子系统开展了全面而深入的研究；一般而言开放量子系统将整个体系分为系统和环境两部分,而后从体系的整个哈密顿量出发利用海森堡方程给出整个体系的演化方程,最后利用Born-Markov近似并对方程两端环境部分求偏迹即可得到关于系统部分的约化密度算符主方程。主方程从数学形式看是一种复杂的算符方程,为了求解主方程人们发展出了若干种方法,主要可以分为C-数方法和超算符(Super-Operator Method)方法两大类,然而无论C-数方法还是超算符方法都有着难以克服的缺点,例如C-数方法将主方程转化为F-P方程后求解困难、繁琐且其解并不适用于任意初态,超算符方法则依赖于主方程本身的的Lie代数结构,因此若主方程不具有Lie代数结构则超算符方法不再适用,这一缺点大大限制了超算符方法的应用范围。综上所述,我们选择了主方程的求解作为研究开放量子系统的切入点,经过大量的推导计算后,我们提出了新的Ket-Bra纠缠态方法(Ket-Bra Entangled Stste KBES Method)用于求解主方程；Ket-Bra纠缠态方法能够将主方程转化为类薛定谔方程(Schrodinger-like Equation)并求解,与C-数方法和超算符方法相比,Ket-Bra纠缠态方法有如下优点：1. Ket-Bra纠缠态方法方法应用范围广,理论上能求解任意有限维能级系统的主方程；而超算符方法则依赖主方程的Lie代数结构,即使主方程的细微改变即可导致超算符方法不再适用。2. Ket-Bra纠缠态方法求解过程简单方便、物理意义清晰明了其解适用于任意初态,且主要计算可以通过计算机完成：3. Ket-Bra纠缠态方法能够将主方程转化为薛定谔方程,这使得求解薛定谔方程的成熟方法同样可用于求解主方程,例如演化算符法、定态方法、微扰法、不变算符法等方法都可通过Ket-Bra纠缠态方法求解主方程,尤其定态方法更能直接给出主方程的最终稳定态。随后我们利用此Ket-Bra纠缠态方法求解了若干开放量子系统的主方程,包括含时外场中的二能级原子的耗散主方程、三能级的V型原子耗散主方程、2-Qubit XYZ型开放自旋链的主方程、N-Qubit XXZ型开放自旋链主方程等,并对这些系统的退相干过程和退纠缠过程进行了研究,研究结果显示系统内部的相互作用会导致其在纠缠演化过程中出现纠缠死亡(Entanglement Sudden Death简称ESD)和纠缠复活(Entanglement Sudden Birth简称ESB)现象,且这种来自系统内部的子系统间的相互作用能在一定程度上抑制系统的退相干和退纠缠过程,尤其对2-Qubit XYZ型开放自旋链的研究更显示即使在t→∞时,系统仍能保持一定的纠缠。对含时外场中二能级原子研究发现,即使在马尔科夫近似下且系统内部不存在任何相互作用,通过对系统施加含时外场仍然可以使系统出现纠缠复活现象；这些研究表明通过系统内部的相互作用或对系统施加外场来抑制退相干的方案在理论上具有一定的可行性,有助于人们在退相干问题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.

【学位授予单位】：中国科学技术大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：O413

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