Quantum Information Processing Based On Weak Cross-Kerr Nonlinearity

Quantum information processing applying only linear optical methods is implemented with low-efficiency and complicated steps. Cross-Kerr nonlinearity affords the interaction between individual photons. Quantum information processing based on weak cross-Kerr nonlinearity is one of the hot topics to fulfill the tasks of photonic quantum information processing in the international forefront of quantum information field.In this dissertation, the deterministic or random quantum key distribution protocols and a quantum privacy comparison protocol are first proposed, where the application of nondemo-lition parity analysis enhances their efficiencies. Based on cross-Kerr nonlinearity, a controlled not gate and a controlled phase gate with low-cost and high-efficiency are constructed, which are the key parts of quantum information processing. Discarding the assistance of photons and exploiting classical feed forward, the protocol is feasibly realized with the probability nearly approaching unity. Applying controlled phase-flip gate and entanglement gates, the preparation, linking, and unlinking schemes of polarization-entangled cluster states are pre-sented. By employing double cross-Kerr nonlinearities and photon-number measurement, the performance of the quantum controlled phase gate is improved, which reduces the difficulty of physical implementation and the error probability, and as its application, the scheme of quantum Fourier transform is designed. Explicitly, the content of the whole dissertation is organized as follows:The first chapter is an introduction. Research background and significance of this dis-sertation is first reviewed. Secondly, the potential candidates of physical carriers of quantum information are presented. Thirdly, quantum information processing based on nonlinear op-tics is introduced. Finally, the main research works and the organization of this dissertation are given.The second chapter provides the foundation of quantum information science. It includes the foundation of quantum mechanics; foundation of information; the fundamental concepts and basic knowledge of quantum information science.The third chapter presents two quantum key distribution protocols and a quantum pri-vacy comparison protocol based on weak cross-Kerr nonlinearity. Exploiting nondemolition parity analysis, two quantum key distribution protocols and a two-party quantum privacy comparison protocol with the aid of a third party are put forward. Employing polarization-qubit Bell states as the quantum channel, two participants safely distribute quantum key and compare privacy information without being affected by outside attacks. Owing to the applications of nondemolition parity analysis, the efficiencies are greatly enhanced.The fourth chapter puts forward two-photon polarization-qubit quantum logic gates depending on weak cross-Kerr nonlinearity. One is a two-photon polarization-qubit controlled not gate, the other is a two-photon polarization-qubit controlled phase gate. Classical feed forward is applied to increase their efficiencies; the adoption of displacement measurement reduces error probability; homodyne measurement with mature techniques is feasible to be operated.The fifth chapter proposes the applications of two-photon polarization-qubit controlled phase gate:preparation of polarization-entangled cluster states and quantum Fourier trans-form. Relying on the polarization-qubit controlled phase-flip gate, the distributed entangle-ment gate, the simplified entanglement gate, and other basic logic gates, the schemes for preparing, linking, unlinking the polarization-entangled cluster states are put forth. In ad-dition, the two-photon polarization-qubit controlled phase gate is improved by exploiting double cross-Kerr nonlinearities and photon-number measurement, which reduce the difficul-ty of experiments and the error probability, respectively. As its application, the theoretical implementation of N-photon polarization-qubit quantum Fourier transform is proposed by exploiting cascaded controlled π/2n-1(2≤n≤N) gates and Hadamard gates.Finally, the summary and prospect are presented.