Finding out all locally indistinguishable sets of generalized Bell states

In general, for a bipartite quantum system Cd⊗d and an integer xmlns:mml="http://www.w3.org/1998/Math/MathML">k such that xmlns:mml="http://www.w3.org/1998/Math/MathML">4≤k≤d,there are few necessary sufficient conditions local discrimination of sets generalized Bell states (GBSs) it is difficult to locally distinguish xmlns:mml="http://www.w3.org/1998/Math/MathML">k-GBS sets.The purpose this paper completely solve the problem GBS in some systems.Firstly three practical effective given,Fan,s Wang et al.4⊗4, condition provided, list all indistinguishable 4-GBS provided,and then completely5⊗5, concise one-way obtained,which gives affirmative answer case xmlns:mml="http://www.w3.org/1998/Math/MathML">d=5 proposed by al.