Theoretical Study On The Effect Of Octapartite Entanglement And Loss On Quantum Squeezing Based On Four-Wave Mixing System

Four-wave mixing system is an effective way to generate multipartite quantum entanglement.It plays a very important role in quantum information and quantum precision measurement.In this paper,we propose two systems based on four-wave mixing system: First,the effect of loss on the quantum squeezing of phase-sensitive four-wave mixing systems is studied.Second,based on two symmetrical cascaded fourwave mixing systems,octapartite entanglement is studied.By using the optical beam splitter model to simulate the loss caused by optical transmission and detection,the effect of loss on the quantum squeezing of twin beams in the phase-sensitive four-wave mixing process is theoretically studied.We have studied the effects of different intensity gains,injection power ratios,and phase losses on quantum squeezing in the system.The results show that the quantum squeezing of the system increases with the increase of the intensity gain;with the increase of the injection power ratio,it first increases and then decreases,and all reach the maximum when the injection power ratio ? = 1;The squeezing is maximum at ? = 0,while the maximum quantum inverse squeezing is obtained when the phase ? equals to ?,and loss is more sensitive to quantum squeezing.In addition,we find that under different parameters,as the loss increases,the quantum squeezing of the system decreases.Our theoretical results provide a theoretical basis for the practical application of the phasesensitive four-wave mixing process.We theoretically propose a scheme of two symmetric cascade FWM processes to generate true octapartite entanglement.This scheme uses an optical beam splitter to connect two independent symmetrical cascaded FWM processes.In order to show the entanglement characteristics of this scheme,we first use a graphical calculation of Gaussian pure states to verify that the generated state is an H-state,and then use the derived coupling strength matrix to reveal the internal interactions of the generated states.Then we study the possibility of this kind of scheme producing octapartite entanglement by applying positivity under the partial transposition criterion.We find that there are octapartite entanglements in the entire gain region in this scheme,and the greater the power gain,the greater the degree of entanglement.In addition,we also explored the effect of the transmission rate on the entanglement characteristics of the system and the dependence of the bipartite entanglement on the power gain and BS transmission.Our scheme provides a theoretical basis for experimentally producing true bipartite entanglement.