Probing entanglement in phase space: signature of GHZ states in the Wignerfunction

We show that the value at the origin of phase space of the Wigner function of entangled GHZ states, involving three modes of the electromagnetic field either in the same cavity or in different ones, is a signature of the quan tum character of those states. This multimode Wigner function can be direct ly measured by a simple extension of a method previously proposed by two of the present authors. A single measurement on an atom which crosses the thr ee modes is enough to distinguish between quantum mechanics and local hidde n variable theories.