Quantum Information Processing With Cavity QED And Continuous Variables

Quantum information science is the new related areas of quantum mechanics andclassical information science. By using various coherent properties of quantum sys-tems, quantum information science manifests a novel type of information processing incomputation, encoding and information transmission. Quantum information process-ing is mainly composed of quantum cryptography, quantum computation and quan-tum communication. In quantum computation, one can obviously decrease the com-putational complexity by using quantum algorithm. Besides the quantum gate design,quantum information processing also includes quantum state engineering and quantumstate cloning, the former can provide the entanglement state which we need in quantuminformation processing, and the latter can go further insight in the quantum no-cloningtheorem.So far, quantum information processing has been wonderfully developed in severalsystems, such as optical system, trapped iron, cavity QED, nuclear magnetic resonance(NMR), quantum dots and so on. Among them, cavity QED offers an excellent stagefor quantum information processing. Up to now, quantum non-demolition measure-ment, quantum state preparations, quantum gates and single-photon sources have beenrealized in the experiments with cavity QED. However, there still lots of technologicalproblems to be overcome, so the efficient schemes in the context of cavity QED attracta lot of attentions. Besides the field of cavity QED, the optical technology recently hasbeen rapidly developed by using linear optical devices, homodyne measurement andfeedforward operations. In the continuous variables domain of optical systems, many-body entanglement state preparations, coherent state cloning and quantum teleportationhave been realized in the experiment. In this thesis, we focus on several proposals forquantum information processing in these two fields.1. Quantum controlled-phase gate for atomic and photonic qubits based on cavityQEDIt has been shown that some intractable problems for classical computers can besolved efficiently by quantum computer. For example, using qubits and quantum op-erations, Shor's algorithm can give an exponential speedup for factoring big numbersand Grover's algorithm can provide a quadratic speedup for unordered database search.It is known that two-qubit controlled-phase gates and one-qubit gates are universal for constructing quantum computer. Based on cavity QED, we proposed the two-qubitquantum controlled phase gate for atomic and photonic qubits, respectively. The for-mer can be generalized to N-qubit case with the same interaction time, and the latteris insensitive to the in?uence of atomic spontaneous emission. Meanwhile, we alsodiscussed the in?uence of the system decoherence and showed the gate fidelity versussuch in?uences in these two schemes.2. The cloning of coherent state with known phasesQuantum information science originally investigated discrete variables system.Subsequently, it was extended to the continuous variables systems with infinite dimen-sional Hilbert space. The mainly continuous variables of light in the lab are coherentstate and squeezed state, both of them are widely used in quantum communication. Itis well known that we can not clone an arbitrary quantum state based on quantum no-cloning theorem, which is the foundation of quantum cryptography security. However,we can clone the quantum state as close as possible. We proposed a scheme to achievethe cloning of coherent state with known phases. Compared with the previous proposal,this scheme obviously improves the cloning fidelity by reducing an auxiliary state andusing squeezed vacuum states. Next, in order to simplify the difficulties of experiment,we gave a method to realize the local cloning of coherent state with known phases byusing linear optical devices, homodyne measurement and feedforward operations. Fur-thermore, by employing an additional EPR state, a nonlocal cloning process can berealized.3. Preparation of the pair coherent state with weak cross-Kerr mediaIn quantum communication, quantum computation and quantum cryptography,quantum state is the information carrier, so quantum information processing can bebrie?y seen as a process of manipulating quantum state. We need to prepare and controlquantum state to achieve a certain goal. The pair coherent state is a quantum state withprominent nonclassical properties. It can also violate the Clauser-Horne-Bell inequal-ity based on homodyne measurement. So the experimental realization of pair coherentstate is very practically important. We gave a nonlocal method for generating such statewith two traveling wave fields in distinct districts by using weak cross-Kerr media andon/off detection. When the input states are coherent states, we can probabilisticallygenerate the pair coherent state. This scheme is robust against the low quantum effi-ciency of photon detectors. Moreover, we revealed that two-mode Schro¨dinger cat stateand generalized two-mode correlated photon number state can be obtained by replacingthe input states.