Relation between phase space coverage and entanglement for spin-1/2 systems

Abstract

For systems of two and three spins 1/2 it is known that the second moment of the Husimi function can be related to entanglement properties of the corresponding states. Here, we generalize this relation to an arbitrary number of spins in a pure state. It is shown that the second moment of the Husimi function can be expressed in terms of the lengths of the concurrence vectors for all possible partitions of the N-spin system in two subsystems. This relation implies that the phase space distribution of an entangled state is less localized than that of a non-entangled state. As an example, the second moment of the Husimi function is analyzed for an Ising chain subject to a magnetic field perpendicular to the chain axis.