Nonlocality Of Quantum Entanglement And The Creation, Discrimination And Application For Multi-photon Entangled States

Quantum entanglement is a fundamental physical resource that plays a pivotal role inmany of the most interesting applications of quantum computation and quantum information.This thesis mainly focus on the nonlocality of quantum entanglement for four-qubit systemsand the creation, discrimination and application for multi-photon entangled states. The thesisincludes five chapters and the structure is as follows:In Chapter1, we introduce the general knowledge concerning the description of quantumstate, quantum entanglement, coherent state and optical quantum information processing.In Chapter2, we present two Bell-type inequalities for four-qubit systems with methodof the stabilizer group of quantum states and discuss the situations that two inequalities aremaximally violated, respectively. Under the given experimental setting, using the inequalitieswe investigate quantum nonlocality of several canonical four-qubit entangled states. Moreover,two useful entanglement-nonlocality relationships are obtained, respectively.In Chapter3, we first propose an efficient scheme for creation of three-photonGreenberger-Horne-Zeilinger (GHZ) state with linear optics and cross-Kerr nonlinearitymedia. It is worth noting that the states which have entanglement in both polarization andspatial degrees of freedom are created in our scheme. Based on an improved symmetryanalyzer for two-photon Bell-state and the optical controlled-NOT gates we construct athree-photon state analyzer which can discriminate eight three-photon GHZ states, completelyand nondestructively.In Chapter4, in the regime of weak nonlinearity we present a scheme of the entangler forgenerating any one of the n-photon GHZ states. Interactions of the incoming photons withcross-Kerr media followed by a phase shift gate, a measurement on a probe beam andappropriate local operations using classical feed-forward of the measurement results allowone to obtain the desired states in a nearly deterministic way. Based on the entangler wediscuss an analyzer for multi-photon maximally entangled states, where all of the2nn-photon GHZ states can, nearly deterministically, be discriminated. Also, by using the entangler of n-photon GHZ states we propose two schemes for preparing multi-photonconcatenated-GHZ states. One is to create a km-photon concatenated-GHZ state from akm-photon GHZ state for m is odd. Another is to create the desired states from kmsingle-photon states by using k entanglers of m-photon GHZ states and km-controlToffoli gates.In Chapter5, a quantum information signature protocol based on weak nonlinearity andthe symmetrical quantum cryptography is proposed. A sender can send classical messages andcan judge whether the messages have been modified or replaced by an adversary. When theauthentication of messages is completed, the fact of the communication can neither bedisavowed by the sender nor be denied by the receiver because of the existence of an honestarbitrator.