Entanglement Of Quantum Optical System And Its Applications

As an irreplaceable source for quantum communication, entangled system play ansignificant role in quantum information processing. Entangled photons and entangledcoherentstates(ECS)aretwocrucialwaysinrealizationofquantumqubitsandimportantinformation carriers. In contrast to other systems of quantum information processing,they are easy to be prepared, and can travel in free space as flying qubits, which makesthem prominent in quantum information processing.Generation and measurement of entanglement are the bases of quantum informa-tion processing and the key points of quantum key distribution, quantum teleportation,quantum secret sharing, etc. Generation of ECSs by using Kerr nonlinearity is a crucialway in entanglement generation. Dissipation and decoherence will decrease the fideli-ty of entanglement, affect the production efficiency and the success probability. Usinglinear optical elements is unable to completely analyze photonic entanglement, but thisproblem can be solved through hyper-entanglement. The main point of this article ishow to generate ECSs and analyze photon entangled states, the results are as follows:First, this paper propose a protocol of generating multi-mode ECSs by nonlinearKerr medium, beam splitter and polarizing beam splitter assisted by single photon orentangled photons. And Bell-type, GHZ-type and W-type ECSs are generated. The pro-tocols are investigated with considering the decoherence caused by the dissipation ofphotons, low efficiency of detector and energy loss of coherent state. The entanglementfidelity, amplitude and others with the decoherence and the amplitude of input state aresystematically calculated and discussed. The entanglement of generated ECS are quan-tified through Concurrence and Negativity, and the results are plotted with the amplitudeof input state.Second, this paper presents a new type of multi-mode ECS, namely, χ-type ECS,and propose a protocol of generation with Kerr nonlinearity. And Bell-type inequalitywith respect to χ-type ECS is investigated, the optimal violation against with the am-plitude of χ-type ECS is calculated. The results show strong violation occurs in smallamplitude region.Third, multi-photon GHZ state analysis using hyperentangled states is proposed.Firstly the polarization three-photon GHZ states are analyzed assisted by the degree of freedom of momentum. The photons are transformed by polarization beam splitters andhalf-wave plates which make CNOT and Hadamard operations, then go to the polariza-tion analyzers. According to the response of the detector, the polarization GHZ statescanbe100%distinguished. Theschemeisimplementableusingpresent-daytechnology.Further analysis of three-photon GHZ states in degree of freedom of momentum is in-vestigated, which results the states can be distinguished clearly with ancillary degree offreedomofpolarization. Finally, theprotocolisprovedtobegeneralizedtomulti-photonsituation.