The Differentiation And Application Of Quantum States Based On LOCC

In recent years,quantum information science has attracted more and more attention because of its potential application value and important scientific significance.With the research advance,quantum information science has spawned many new scientific and technological hotspots,and has made remarkable achievements.In quantum information,there is a series of basic issues completely different from classical informations,one of which is about distinguishability of a set of quantum states.Under micro quantum conditions,because of the superposition principle of Hilbert space.The principle makes it possible that quantum states describing different quantum systems are not orthogonal,which bring a series of problems such us quantum local indistinguishability and quantum non-cloning.However,under macro classical conditions,as extremely noisy environment around macroscopic system,system s cannot keep themselves in coherent superposition states.Thus,the states describing these systems are naturally orthogonal but only local operation and classical communication(LOCC)as allowed.This paper is mainly discuss the problem of distinguishing quantum states based on local operation and classical communication(LOCC).LOCC includes local operation(LO),one-way LOCC and completely two-way LOCC.That means when measuring a composite system,the two sides of the measurement are separated from each other.They can only perform quantum operations on their own subsystems and exchange classical information through the classical channel.The main research results in this thesis are as follows.1.We mainly study the distinguishment of orthogonal states in d(?)d bipartite system based on one-way LOCC,and introduce an algorithm to distinguish orthogonal bipartite states by one-way LOCC.Given a group of entangled states in a set of bipartite system,by calculating the subspace associated with this set of entangled states.we can further determine whether the space contains a maximally Abelian subspace.If it dose,we can say that this group of states can be distinguished by one way LOCC.In addition,we mainly focus on the entangled states in 4(?)4 bipartite system on the basis of this general algorithm,and propose a fast algorithm for distinguishing a group of generalized orthogonal Bell states based on one way LOCC.Finally,an example is given to verify the proposed algorithm.The fast algorithm has less complexity than general algorithm and has more practical value.2.We know that the local distinguishment of quantum states has important application value in designing quantum threshold scheme.If a(k,n)-threshold LOCC-QSS wants to resist the unambiguous attack,it must satisfy two conditions,but in fact,it is difficult to select the quantum states which satisfy these two conditions at the same time.The concept of judgment space can weaken the condition,this condition is a little bit strict in practical application.In this paper,we constructed 7 different 5-qudit quantum entangled states under the sense of displacement,calculated their judgment space and proposed the rule of distinguishability of judgment space.With judgmental rules,we studied the discrimination of 5-qudits quantum states based on LOCC systematically and summary the discipline for discrimination of these states.Finally,we choose the appropriate states according conditions and propose a secure(k,n)-threshold LOCC-QSS scheme.The above results provide a theoretical basis for quantum communication.