Experimental Researches Of Quantum Cloning

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.