Wigner function for SU(1,1)

TL;DR

This paper develops a Wigner function formalism for SU(1,1) symmetric systems, enabling potential applications in quantum metrology and providing a method for experimental sampling.

Contribution

It introduces a consistent derivation of the SU(1,1) Wigner distribution from two modes, linking it to displaced parity operators for experimental accessibility.

Findings

Derived a Wigner distribution for SU(1,1) systems

Linked the distribution to displaced parity operators

Demonstrated the formalism with relevant examples

Abstract

In spite of their potential usefulness, Wigner functions for systems with SU(1,1) symmetry have not been explored thus far. We address this problem from a physically-motivated perspective, with an eye towards applications in modern metrology. Starting from two independent modes, and after getting rid of the irrelevant degrees of freedom, we derive in a consistent way a Wigner distribution for SU(1,1). This distribution appears as the expectation value of the displaced parity operator, which suggests a direct way to experimentally sample it. We show how this formalism works in some relevant examples.