The superposition invariance of unitary operators and maximally entangled state

In this paper, we study unitary operators and the superposition of unitary operators. We calculate the the superposition of unitary operators and find that some unitary operators superposition is also unitary operator. Furthermore, via this property, we discuss the set of orthogonal maximally entangled states. For 2,3,4,5-qubit, we introduce the complete sets of orthogonal maximally entangled states. We find that orthogonal basis of maximally entangled states can be divided into k subspaces. It is shown that some entanglement properties of superposed state in every subspace are invariant.