Research On Quantum Secret Sharing Scheme And Distinguishing Method Based On Local Distinction

The concept of quantum cryptography was proposed by Bennett et al.in 1984.Quantum cryptography based on classical cryptography and quantum mechanics is used to realize unconditional information safety.Quantum secret sharing is an important research direction of quantum cryptography.The idea of quantum secret sharing is:Suppose the distributor needs to send secret information(classical or quantum)to multiple participants,only a few authorized participants can recover secret information while individual or non-authorized participants cannot.In 1999,Hillery et al.used the quantum correlation of GHZ triplet to propose the first quantum secret sharing scheme.After that many domestic and foreign experts begin to invest into its research,and have made a lot of scientific research,so that it has been widely developed and applied.Main contributions of this paper are summarized as follow:(1)We mainly study the construction of six-qudit quantum entangled states and their local distinguishability.We construct eleven kinds of six-qudit quantum entanglement states,calculate their judgment space,and propose a distinguishability rule of judgment space.Based on this rule,we study the local distinguishability of the eleven kinds of six-qudit quantum entangled states.Based on R.Rahaman et al.'s {k,n)threshold quantum secret sharing model,we propose a(k,n)threshold quantum secret sharing scheme which can resist unambiguous attacks.Finally,we analyze the security of the scheme from four aspects:intercept-and-resend attack,dishonest participant attack,Trojan horse attack and entanglement-and-measure attack.(2)In view of Tanmay et al.'s one-way LOCC distinguishability conclusion of two-partite orthogonal states,it is clarified whether there is a one-way LOCC protocol depends on whether a subspace composed of a Heimitian matrix contains a maximally abelian subspace.According to this conclusion,the distinguishability of one-way LOCC for all the orthogonal states in dA(?)dB can be judged.Based on this,we propose a general method to judge whether generalized Bell states can be distinguished by one-way LOCC.Finally,we give two examples.