Non-negative Wigner functions for orbital angular momentum states

I. Rigas, L. L. Sánchez-Soto, A. B. Klimov, J. Řeháček, Z. Hradil
2010 Physical Review A. Atomic, Molecular, and Optical Physics  
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.
doi:10.1103/physreva.81.012101 fatcat:g2vjzqgpezawtmik5ya2otrqru