A comparison of two nonclassical measures, entanglement potential and the negativity of the Wigner function

Two measures of nonclassicality, the entanglement potential and the negativity of the Wigner distribution function defined by the volume of its negative domains, are compared based on an investigation of the nonclassicality for Fock states and Schrödinger cat states in a decoherence process. Both the entanglement potential and the total negative probability are reduced in the linear loss process and the partial negative distribution of the Wigner function is wiped out for large losses while the entanglement potential is always positive. We give a bound condition and find that, though not yet mathematically proven in general, the upper bound of 50% is the maximum allowed loss for the survival of the negative distribution of the Wigner function.