A Study Of Entangled Character Of Multi-mode Entanglement

Quantum entanglement is an interesting phenomenon which occurs among multitude particles, that is to say, the measuring outcome to one particle cannot be independent of the measurement parameter of the others.Based on the fundamental principle of entanglement as well as the widely acknowledged views in the literature, this paper defined entanglement from different respects,presented an explicit explanation to the measurement of two-particle system entangled pure state, and worked out the nonlocality and the degree of entanglement. Since it is difficult to measure entanglement under the state of multi-modes, this paper adopted Wigner quasi-probability distribution function and calculated the Wigner function of coherent state, two-mode squeezed state and multi-mode coherent state. This paper employed a new method to calculate Wigner function distribution, which made use of the construct vectors to work out Wigner function. To prove its reliability, this paper adopted this method to draw the pictures of the coherent state and Schr?dinger-cat state and the result is consistent to most literature. Besides, through observing the Wigner function of the multi-mode coherent state, it is found that first, it is possible to gain a visual picture of coherent relationship among the coherent states, that is to say, they are correlated with each other; second, compared to the Wigner curved surface of the coherent states, multi-mode coherent state shrinked in some direction, while in another direction, expanded so that the original symmetry was destroyed. Besides, Bell local condition was employed to analyze the energy levels of three-particle GHZ state, which received a different result from that with Hamilton.