Abstract:

Quantum communication is a kind of communication method which encrypts and transmits information by using quantum effect. The subject has gradually moved from theory to experiment, and has developed to practicality. People pay more and more attention to efficient and secure information transmission. In 1993, six scientists from different countries proposed a scheme to realize quantum teleportation by combining classical and quantum methods. In this scheme, the nonlocality of entangled states plays an important role. This characteristic beyond ordinary cognition constitutes the basic resource of secure quantum communication. Orthogonal quantum states of composite systems may not be locally distinguished as one of the important manifestations of quantumnonlocality.This paper is devoted to thestudy of the local indistinguishability of orthogonal product basis quantum states ind$\otimes$d. In this paper, we construct another class of local indistinguishable orthogonal product basis quantum state fora$\otimes$d(d>2) quantum systems, which contain 3(d-1)orthogonal product states. We will prove that these states are locally indistinguishable by a simple and efficient method.This result also demonstrates the phenomenon of nonlocality without entanglement.

Key words: local operations and classical communications, orthogonal product basis quantum states, quantum nonlocality, threshold scheme