【作者】 王志伟；

【导师】 郭光灿；

【作者基本信息】 中国科学技术大学 ， 光学， 2008， 博士

【摘要】 量子信息学作为一门新兴的并迅速发展的学科,将信息学和量子力学成功的结合起来,利用微观粒子的量子力学原理来解决经典信息学和经典计算机所不能解决的问题。由于其潜在的应用价值和重大的科学意义,量子信息学作为最近十几年来迅速发展起来的新兴学科,正在越来越多引起各方面的关注。而纠缠在量子信息学中扮演着极为重要的角色并且在量子信息理论的运用中其核心作用,例如量子密码,量子通信,量子计算。纠缠也是量子信息论区别于经典信息论的重要特征之一。纠缠如此重要,那么如何从理论及实验上上定义纠缠,度量纠缠,和探测纠缠就构成了量子信息论的最基本的内容,也是该领域研究的热点和难点。本博士论文着手于量子信息过程中量子态及量子演化过程的描述以及纠缠的描述、探测、度量及其操作,具有以下几个主要内容:1.纠缠操控量子体系不可避免的会和外界环境相耦合,导致消相干,实际上应用的量子态一般是非最大纠缠态,或者混态,或者两者兼有。为了更好的把纠缠应用于量子信息处理等过程,就需要我们对实际中的纠缠源进行操纵,提纯,使其达到我们的需求。总体来说,有两种纠缠蒸馏或纯化的协议:一种是对单个拷贝进行操作,这种协议被归类为过滤协议(Filtering Protocols),我们从实验上首次验证了针对两量子比特混态的最佳过滤协议并证明了通过过滤操作能够有效的增加系统的纠缠度;另一种是对多分拷贝进行操作,如每步同时对两份拷贝进行操作的循环协议(Recurrence Protocols)。纠缠纯化不仅具有理论上的意义,还有很重要的实用价值,可以建立无条件皓勺密钥分配协议,构建量子中继器,提高量子计算中的错误阈值等等。2.纠缠探测和度量纠缠探测和度量是量子信息中的一个核心的问题。结合我们的工作介绍了实验上常用的纠缠探测和度量的方法,如纠缠见证算符的局域分解,利用光学干涉仪来直接实现纠缠见证算符的测量,利用不确定关系不等式来探测和度量纠缠,以及双份拷贝向反对称子空间的投影等等,这些方法结合具体的实验环境能够有效的减少测量次数,更直接的对系统的信息做出判断和估计,在应用方面具有重要的意义。我们不仅讨论了分离变量的纠缠探测和度量,还研究了一类特殊的自发参量下转换过程中连续变化横向动量间的纠缠,这其中涉及的更多的是泵浦光和参量光的频率谱信息和空间分布信息,这对操控参量光的空间分布和频率关联类型有重要的影响。3.纠缠在动力学中应用纠缠在描述系统量子状态及其动力学演变过程中也有重要的应用,这也是系统量子特性之一。我们介绍了描述系统演变的理论方法,一种是通过对系统的整体信息进行测量然后进行估计的即量子过程层析,另一种是借助纠缠特性来直接描述动力学过程的DCQD,后一种方法能够有效的减少测量次数并且可以通过较少的测量直接提取系统的部分信息,在高维的情况下算法的加速效果更为明显。更多还原

【Abstract】 Quantum information is one new-rising and fast-developing subject, as a successful combination information science and quantum mechanics, which can be used to solve problems that classical computer cannot address. Quantum information is attracting more and more attention due to the great potential applications and significant scientific influence.Entanglement plays an important role in quantum information processing, such as quantum cryptography, quantum communication, and quantum computation. Entanglement also serves as a one of the greatest features that distinguish quantum information from classical information theory. Entanglement is so important that how to define, quantify, and detect entanglement both in theory and experiment becomes the basic task and hot topic in quantum information.The dissertation are focusing on the characterization of quantum states and their evolving dynamical process, as well as the concept of entanglement, the detection and quantification of entanglement. The main results of the dissertation are as follows:1. Entanglement operation.Quantum systems will unavoidably interact with external environment leading to decoherence. In general, the practical quantum state is non-maximally entangled states or mixed states, or both. In order to make full use of entanglement states, we have to operate on the practical entangled states at hand, i.e. purify entanglement, such that the entanglement can meet our criteria in practical application.Generally speaking, there are two kinds of entanglement purification or distillation protocols. The first kind of protocols involves the operation on single copy of entangled states, which is also called as Filtering Protocols. We experimentally implement the optimal filtering protocol and show that filtering operations can effectively increase entanglement. The second kind of protocols need the operation on many copies of quantum states, such as simultaneous operation on two copies, Recurrence Protocols.The importance of entanglement purification exists in not only quantum information theory, but also in the practical applications. It can build unconditional quantum key distribution protocols, constitute quantum repeaters, and improve the error threshold in quantum computation. 2. Entanglement detection and quantification.Entanglement detection and quantification is another key problems in quantum information. Combined with our works, we introduce the common entanglement detection and quantification methods which is frequently used in experiments, such as the local decomposition of entanglement witness, optical interferometer for direct observation of entanglement witness, the uncertainty relations, and the projecting into the antisymmetric subspace consisting of two identical copies. These methods working in the special experimental scenario can effectively reduce the measurement times and estimate the information about the quantum systems directly. In practical cases they may have important applications.We not only discuss entanglement detection and quantification for discrete variables entanglement, but also for one special kind of continuous variables entanglement, which rises from the transverse momentum entanglement between the signal and idler photon produced in Spontaneous Parametric Down Conversion process. It involves the relation between the spatial and spectral information of the pump light and that of the down-conversioned photons, which can help to control the distribution of down-conversioned photons and its frequency correlation type.3. The application in quantum dynamics.Entanglement is also helpful in characterizing the state and dynamical process of quantum systems. We introduce two methods in characterizing dynamical process of quantum systems. One method is quantum process tomography which requires quantum state tomography on a set of input states and subsequent reconstruction of quantum process matrix on these data; another method is Direct Characterization of Quantum Dynamics (DCQD), which is based on input entangled states and Bell states measurement at the output. We experimentally perform quantum dynamical process measurement with the two methods and show it can reduce the experimental configurations by a factor of 2 compared with that of standard quantum processing tomography (SQPT). The algorithm works better when ideal Bell state measurement is adopted since in optical experiment we can only perform partial Bell state measurement.更多还原