Complete Bell State Analysis With Linear Elements

Bell state measurement is an important part of quantum information research,such as quantum teleportation,quantum dense coding and so on.Previous studies have shown that,Bell states can only be recognized at most50%,only based on linear optical operations,such as beam splitter half-wave plates.With the help of pairs of auxiliary photons,Bell states can be distinguished 75% or more efficiently.With the help of multiple degrees of freedom,Bell state discrimination efficiency will reach 100%.For example,the efficiency can be improved to 100% by using the hyperentanglement scheme,but the scheme is more complicated.Therefore,it is still a hot issue to realize the complete Bell state measurement scheme which is simple and easy to operate.The hybrid beam splitter coupled with different degrees of freedom can distinguish the two Bell states that cannot be distinguished by ordinary beam splitter,which plays an important role in Bell state measurement.Based on which,we propose a new scheme to achieve a 100%Bell state measurement if a Bell state copy can be prepared successfully.The specific contents of this paper are as follows:In chapter one,we give an introduction which summarizes some previous works on Bell state measurement,including the research scheme of Bell state measurement using linear and nonlinear elements.There are also two parts to describe the linear works.One is to perform Bell state measurement on a single degree of freedom.This operation can only identify50% of the Bell state.The other part is to introduce multiple degrees of freedom to measure the Bell state on a certain degree of freedom.In chapter two,we introduce the hybrid beam splitter.The hybrid beam splitter is the key tool for the complete Bell state measurement in this paper.It couples the polarization and momentum of particles,which can change both polarization and momentum.In chapter three,we explain how to use linear element to realize the complete measure of Bell state.Firstly,the Bell states to be measured is successfully duplicated by the means of the quantum cloning into two same parts.Secondly,one through ordinary beam splitter(BS),and another through hybrid beam splitter(HBS),and then they respectively go through a detector.Due to the the complementary effects of the two beam splitters.At last,four kinds of Bell states can be easily distinguished by combining measurements results of the detecters.Finally,in chapter four,we summarize our work and look forward to the future research work.And the further research would focus on the effect of Bell state replication on Bell state measurement by using quantum cloning.