The Construction Of Unbiased Unextendible Maximally Entanglement Bases Research In Bipartite Systems

Measurement basis is an important content of quantum information.Among them,unbiased basis is the best measurement basis,and it is widely used in many fields.In recent years,the study of unbiased base has shifted from a simple single space to bipartite systems.Compared with the single system,the structure of the unbiased base in the bipartite systems become more complicated.How to construct the unbiased base in the bipartite sys-tems has attracted many scholars interest.The current physical system is not just 2 dimension.Therefore,how to construct the measurement base has realistic physical meaning and applica-tion value in high-dimensional physical systems.At the same time,based on the study of the existing bipartite systems,the construction problem is studied about the unbiased unextendible maximally entangled bases.The main results are as follows:(1)Unextendible maximally entangled bases are constructed in bipartite space C~2(?)C~5.Specific ideas:a set of unextendible maximally entangled bases in bipartite space can be con-structed,by preserving the standard orthogonal basis of the space C~5 and changing the standard orthogonal basis of the space C~2.(2)Unextendible maximally entangled bases are constructed in bipartite systems C~3(?)C~4.The process is to first give a general expression of the unextendible maximally entangled bases.And then,by changing the standard orthogonal basis of the space C~3 or C~4,three groups of unexpandable maximum entangled bases can be obtained while satisfying unbiased.(3)Unextendible maximally base are constructed in Bipartite systems C~4(?)C~5 and C~3(?)C~8.By preserving the standard orthogonal basis of the space C~4(C~3),and changing the standard orthogonal basis of the space C~5(C~8),a set of unextendible maximally entangled bases can be constructed while satisfying unbiased.(4)Based on the above construction methods.In the general bipartite systems C~3(?)C~3l4(l ?Z~+),the construction is studied about unextendible maximally entangled bases,and obtain a set of unbiased unextendible maximally entangled bases.