Local Indistinguishability Of Orthogonal Product States

Quant um information is an emerging research branch.It is a novelinterdiscipline in many fields such as quantum meehanies,mathematies,information theory andcomputer theory,The problem about local distingnishability of quantum states is one of the hot topics in quantum information theory,which provides very important theoretical support for quantum seeret communication.The so-called local discrimination means that in a known set of bipartite or multipartite orthogonal product states,different particle of a quantunn state is held by different people(they maybe met long ago but now live far apart).They expcet to determine the quantum state by measuring the partielcs in their hands,afterwards they can only send classical information to each over a classical communication channel.In this paper,we mainly study local indistinguishability of orthogonal product states in the tripartite systems,and the following conehusions are drawn.First,in tbe Cd(?)Cd(?)Cd(d?3)quantum system,we construct 3d-2 orthogonal proluct states,and prove that they cannot he perfcectly distinguished by local operations and classical communication(LOCC).Next.we construct 3d+4 LOCC indistinguishable orthogonal product states in the Cd(?)Cd+1(?)Cd+2(d?3)quantum system.Finally,for the general tripartite quantum system Cn1(?)Cn2(?)Cn3(3?n1?n2?n3).we present 2(n2+n3-1)-n1 orthogonal product states and prove that they have local inlistinguishability by using a very simple and and artful method.Meanwhile,we give a generale,we give a general method to construct LOCC indistinguishable multipartite orthogonal product states sets in Cd1(?)Cd2(?)...(?)Cdn(d1,2...n?6).Our conelusions further optimize the existing results.