摘要
量子信息学是量子力学与信息科学相结合的一门新兴交叉科学。同经典计算机相比,量子计算机在一些方面具有独特的优势,例如可以有效解决某些对于经典计算机来说属于难解完全类的问题,以及可以较容易的模拟量子系统的行为。由于量子信息与量子计算所存在的巨大应用潜力,因而激发了研究者对此研究领域的极大兴趣同时也引起各国政府、科学界和信息产业界的高度重视。
1982年,Wootters和Zurek提出了量子不可克隆定理,证明对于一个完全未知的量子态进行精确的克隆是不可行的。这条定理的提出奠定了量子安全密钥分配方案的理论基础,从而也引起众多科学家对于量子克隆领域深入研究的兴趣。到1996年,Buzek和Hillery提出近似克隆机的理论模型,更引发了对于量子克隆理论和实验方面研究的热潮。由于量子克隆操作对于量子态的精密操控有着较高的要求,在实际的实验中需要对脆弱的量子体系进行相干操作和控制,因此要建立一种能够满足要求的量子克隆机是非常困难的。从现有的实验方案来看,液体核磁共振(Nuclear Magnetic Resonance)技术是目前最为成功的量子信息处理手段之一。利用核磁共振系统成熟的技术条件,在量子克隆领域做一些相关的研究工作,特别是此过程中积累的丰富的量子相干控制技术,为量子克隆机乃至下一代的量子计算机的发展提供可借鉴的经验,同时也将增进我们对实际量子信息过程以及它的强大功能的理解。这也正是我选用液态NMR技术实验实现量子克隆机做为博士论文研究主题的重要原因。本论文在核磁共振系统中实现量子克隆机的实验研究中取得以下几个方面的研究成果:
1.实验实现1→2的非对称phase-covariant量子克隆机
作为近似克隆的一种,非对称克隆可以实现信息量在输入态和克隆拷贝间直接的传输控制。克隆态的保真度以及克隆过程对于初始态的破坏都依赖于控制参数的调节:即如果我们提高克隆态的保真度,那么同时对于初始态的破坏也会增加。这种信息交换关系决定了窃听者可以从一个有着一定误差率的信道中最多可以获取多少信息。在此论文中,我们构建了可以实现最佳1→2的非对称phase-covariant量子克隆的量子逻辑网络。克隆过程在NMR系统中通过使用核自旋作为量子比特实验实现并同时证明了输出态的保真度之间关系。实验中,我们设计了循环路径得到几何相门实现克隆过程。这种几何相门已被证明对于系统的一些随机扰动具有抵抗作用从而可以提高实验的保真度。
2.实验实现1→2的概率克隆机
量子克隆可以分为两大类:近似克隆和概率克隆。近似克隆以1的概率得到量子态的近似拷贝,而概率克隆则以小于1的概率得到量子态的精确拷贝。目前关于近似克隆的实验在光学和核磁共振体系中都有很多实验研究。但是由于复杂的逻辑网路和精确的实验操控的要求,对于概率克隆实验实现却一直没有进展。在此论文中,通过设计一个有效简化的逻辑网路并应用强调制脉冲和相循环技术,我们成功的在核磁共振系统中实验实现概率克隆机。实验的克隆效率和克隆态的保真度都与理论非常吻合,并且验证了克隆效率与输入态集的交迭度(overlap)的关系。
Quantum information is a new subject from the combination of quantum mechanics and information science. Compared with classical computers, quantum computers manifest distinct advantages in many respects, for example, to cope with some certain problems which are NP problems for classical computers and to simulate the evolution of quantum system. The resultantly powerful abilities have intrigued enormous interest in this field of research and become the various governments, science societies and information industrial circles.
In 1982, Wootters and Zurek propose no-cloning theorem, which states that no quantum operation exists that can duplicate perfectly an arbitrary quantum state. The no-cloning theorem is a direct consequence of the superposition principle and linearity of quantum mechanics. The impossibility to duplicate an unknown quantum state without introducing noise is exploited by the modern quantum communication protocols and lies at the heart of the security of quantum key distribution schemes. Although perfect copying is forbidden one may nevertheless copy the states in an approximate way. The optimal quantum cloning machine introduced by Buzerk and Hillery in 1996 yields clones whose fidelity with respect to the input state is the maximum possible. Since then, the quantum cloning has been investigated by numerous authors. Though it needs precise operation to realize cloning process, the coherent manipulation and control of the fragile quantum system in the actual experiments, practically building quantum cloning machine has proved extremely difficult. However, of the extant methods, liquid-state Nuclear Magnetic Resonance (NMR) is arguably one of the most successful physical systems. Now, the achievements on liquid-state NMR QIP, especially the rich source of basic quantum control techniques accumulated for QIP, will contribute to realization of the quantum cloning machine and the next generation of quantum information processors, especially for the understanding of the power of quantum information processing. Therefore, I choose the liquid NMR system as the tool of the research of the quantum information, and focus on the experimental realiza- tion of quantum cloning machine as the subject of my dissertation.
In this thesis, we aim at the experimental realization of quantum cloning machine in NMR system. Our results focus mainly on the following two issues:
1). Approximate cloning can be optimized in different ways. In so-called asymmetric cloning, the amount of information transferred from the input state to the copy is an adjustable parameter. The quality of the copy and the distortion that the cloning process causes on the original system both depend on this parameter: if the quality of the copy increases, the distortion of the original necessarily increases simultaneously. This is quantified by the fidelity of the two output systems, which is defined as the overlap of these states with the input state. This tradeoff relates, e.g., the amount of information that an eavesdropper can extract from a quantum communication channel to the error rate of the transmitted information. In this thesis, we construct a two-qubit quantum logic circuit that implements the optimal asymmetric 1→2 phase-covariant cloning for arbitrary input phase. Our cloning machine does not require any ancilla qubits and uses only two gate operations. The cloning process is implemented experimentally in an NMR system, using nuclear-spin qubits and the trade-off in fidelity for the two output qubits is also demonstrated. For the cloning operations, we used cyclic rotations of the qubits in such a way that the system acquired a geometrical phase. This procedure has been proposed for shielding the gate operation from such perturbations that leave the area of the quantum mechanical trajectory invariant and thereby improve the overall fidelity.
2). The approximate quantum cloning may be divided into two main categories: quantum imperfect cloning and probability quantum perfect cloning (PQC). An quantum imperfect cloning machine can copy quantum information in an imperfect way with probability equal to 1. Probability quantum perfect cloning (PQC) can produce perfect copies with some probability less than 1, e.g. nondeterministic. Various imperfect cloning machines have been demonstrated with linear optics and NMR. However, to obtain a physical means to carry out the probability quantum perfect cloning PQC is still challenging due to its requirements of complicated network and precise controlling. In this thesis, by effectively simplifying the network and using the combinations of SMP and phase cycling techniques, we succeed with the experimental realization of perfect cloning with optimal deterministic probability in NMR system. The measured fidelities of clone states and its cloning efficiencies well agree with the theoretical prediction and the connection between cloning efficiency and the overlap of the input states is also experimentally proven.
引文
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