The Construction Of Mutually Unbiased Bases In Quantum System

According to "national medium and long-term program for scientific and technological development",from 2006 to 2020,known as" quantum control research",one of the important research content is quantum informatics,which is an interdis-ciplinary subject of quantum mechanics and informetics[1].Thanks to its important application in the field of quantum communication,quantum computation and incomparable great potential,quantum mechanics become an international research hotspot in recent years.To get the state of a quantum system(get the information of the corresponding unknown state),one needs to perform a series measurement on a large number of identically prepard copies of the state,because of the No-cloning Theorem.This kind of measurement is the projection of quantum states onto different bases,and the characteristics of unknown quantum state are judged by the projection.There are many different kinds of measurement,and the unbiased base is the best measurement(i.e.,no waste).It has been widely used in the quantum information processing,the Wigner function,quantum error correcting code and cryptographic protocols,etc.Quantum entanglement is an important concept in quantum information science,a unique physical feature of quantum mechanics.Because of the unique physical properties of entanglement,that quantum information have more new features,then classic informatics does not have.Quantum entanglement in quantum mechanics and quantum information theory has a particularly important features,quantum information processing,etc,also depends on the maximum entangled.Thus in recent years,the problems combinated the unbiased with entanglement are more and more important and have become a research hotspot.In this paper,fistly,we introduce the mathematical knowledge and physics concepts related to the subject,as well as relevant history and current situation of the development.Secondly,in the bipartite quantum system with the same dimensions,we study the MUMEB,and introduce the way of the construction of MUMEB in the bipartite system with low dimension.On the other hand,we construct MUMEB in C3(?)C9 from MUMEB in C3(?)C3,and generalize the methord,i.e.,A systematic 'way of constructing MUMEBs in Cd(?)Cdk from MUMEBs in Cd(?)Cd,have been presented.Finally,A systematic way of constructing MUMEBs in Cd(?)Cmld' from MUMEBs in Cd(?)Cd',have been presented.