Non-negative Wigner functions for orbital angular momentum states

TL;DR

This paper demonstrates that for the angle and angular momentum quantum pair, only eigenstates of angular momentum have non-negative Wigner functions, contrasting with the Gaussian case in continuous variables.

Contribution

It reveals a unique property of angular momentum states, showing that non-negativity of the Wigner function is exclusive to eigenstates, unlike the Gaussian case in continuous variables.

Findings

Only angular momentum eigenstates have non-negative Wigner functions.

Contrasts with continuous variables where Gaussian states are non-negative.

Discusses implications for quantum state characterization.

Abstract

The Wigner function of a pure continuous-variable quantum state is non-negative if and only if the state is Gaussian. Here we show that for the canonical pair angle and angular momentum, the only pure states with non-negative Wigner functions are the eigenstates of the angular momentum. Some implications of this surprising result are discussed.