The Mutually Unbiased Base In The Bipartite Quantum System

Quantum information theory is a cross field of quantum mechanics,cryptography,classical information theory and mathematics.Quantum entanglement is a special con-cept in quantum information.It plays a very important role in quantum informatics.In recent years,quantum entanglement combined with mutually unbiased basis has created a new concept,mutually unbiased unextendible maximally entangled bases and mutually unbiased maximally entangled bases.In this thesis,the construction of the maximal entanglement basis in the Cd(?)cd’(d’ =kd,k∈Z+)is studied.It is also found that the mutually unbiased problem of the two set of maximal entanglement basis in Cd(?)Cd’ can be converted into the transition matrix A with two orthonormal base in Cd’:(?)Then,a systematic way of constructing MUMEBs in Cd(?)C3ld’(l∈Z+)from MUMEBs in Cd(?)Cd’(d’=kd,k∈C+).Finally,we study the unbiased problem of unextendible maximally entangled base.A general approach to construct MUUMEBs in Cd(?)C3ld’(l∈Z+)and Cd(?)Celd’(e∈Z+,l∈Z+)from MUUMEBs in Cd(?)Cd’(d’=kd,k ∈ Z+)have been introduced.The concrete form of two set of mutually unbiased UMEBs in C4(?)C15 is also given.