Searching for an absolutely maximally five-level entangled state

Entangled states play an important role in quantum computation and information. In this paper, for a five-level entangled state, we define some unitary operations and give an operator multiplication. With the help of the unitary operation, we obtain some local unitary equivalent bipartite and tripartite five-level absolutely maximally entangled states (AMES). Furthermore, by using recurrence relations, some four-partite and five-partite five-level AMES can be constructed.