Even- and odd-orthogonality properties of the Wigner D-matrix and their metrological applications

The Wigner D-matrix is essential in the course of angular momentum techniques. We here derive the new even- and odd-orthogonality properties of the Wigner D-matrix which was yet to be demonstrated in textbooks and also apply them to identifying optimal measurements for linear phase estimation based on two-mode optical interferometry with two specific quantum states.