Quantum Entanglement Based On The Dual-mode Waveguide Optical Transverse Mode Of The Classic Analog

Quantum entanglement is one of the most fundamental and most special properties of quantum mechanics;it attracts wide attentions and in-depth researches due to the importance of quantum entanglement in quantum information.In this paper, we first introduce quantum information, the properties of quantum entanglement and the importance of quantum entanglement in quantum information. Then we introduce a quantum computation scheme based on optical transverse modes in multimode waveguide. In the scheme, quantum bits are encoded by using optical transverse modes, and CNOT gate is implemented by using nonlinear optics. Based on this, we propose a new conception of the so-called "mode-entangled states" to realize the classical simulation of quantum entangled states, which can be produced by CNOT gate or linear optical components. Further, we study some properties of the mode-entangled states. The main work of this paper is as follow:First, we simulate the nonlinear optical scheme using finite difference beam propagation method, and obtain correlation function of the two fields in mode entangled states based on correlation measurement of Bell inequality, the correlation function violate the Bell inequality, which proves there is nonlocal correlation between the two fields. Thus, the mode entangled states can be regarded as the classical simulation of the quantum entangled states. Further, we use an ensemble labeled by phase difference to describe mode entangled states.After that, we proposed a new scheme based on linear optics to realize mode entangled states. The numerical simulation results show that the correlation function of mode entangled states is quite similar to quantum entangled states, which can violate the Bell inequality. This scheme has proved that the phase difference ensemble can be used to describe the nonlocal correlation, and the nonlocal properties may originate from the random phase mechanism.And then we generalize the linear optical scheme to realize the GHZ states of three particles using three classical fields. According to GHZ theorem, the full correlation of three particles can give the nonstatistical criterion of quantum entanglement, which is more reliable than Bell inequality, which is based on statistical property. Further, we obtain the nonstatistical criterion of nonlocal correlation of mode entangled states, which again prove the validity of using classical fields to realize the classical simulation of quantum entanglement.The nonlinear and linear optical schemes proposed in the paper can be carried out in current condition;hence we have some experimental research to prepare the experimental verification. At last we give some discussion and conclusion.