Wigner Functions for Arbitrary Quantum Systems

The possibility of constructing a complete, continuous Wigner function for any quantum system has been a subject of investigation for over 50 years. A key system that has served to illustrate the difficulties of this problem has been an ensemble of spins. While numerous attempts have come close to generating a complete Wigner phase-space description for such a system, each has either been artificial in its construction or restricted in its applications. Here we present a general method of constructing Wigner functions that can be used to fully describe quantum spin systems of any dimension or ensemble size.