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

TL;DR

This paper derives new even- and odd-orthogonality properties of the Wigner D-matrix and applies them to identify optimal measurements in quantum optical phase estimation.

Contribution

It introduces previously unreported orthogonality properties of the Wigner D-matrix and demonstrates their application in quantum metrology for phase estimation.

Findings

Derived new orthogonality properties of the Wigner D-matrix

Identified optimal measurements for linear phase estimation

Applied properties to two-mode optical interferometry

Abstract

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.