Construction of Complete Orthogonal Genuine Multipartite Entanglement State**Supported by the National Natural Science Foundation of China under Grant Nos 11775177, 11775178, 11647057 and 11705146, the Special Research Funds of the Department of Education of Shaanxi Province under Grant No 16JK1759, the Basic Research Plan of Natural Science in Shaanxi Province under Grant No 2018JQ1014, the Major Basic Research Program of

Abstract

With the development of quantum information processing, multipartite entanglement measures are needed in many cases. However, there are still no complete orthogonal genuine multipartite entanglement (GME) bases available as Bell states to bipartite systems. To achieve this goal, we find a method to construct complete orthogonal GME states, and we exclude many equivalent states by leveraging the group theory. We also provide the case of a 3-order 3-dimensional Hilbert space as an example and study the application of general results in the dense coding scheme as an application. Moreover, we discuss some open questions and believe that this work will enlighten extensive studies in this field.