Entanglement entropy of a scalar field in a squeezed state

Abstract

We study the entanglement entropy within a spherical region for a free scalar field in a squeezed state in 3 + 1 dimensions. We show that, even for small squeezing, a volume term appears, whose coefficient is essentially independent of the field mass. This is in line with Page’s argument that the entanglement entropy in an arbitrary quantum state is proportional to the number of degrees of freedom of the smaller subsystem. It follows that squeezed states can be considered as arbitrary quantum states, in contrast to the ground or coherent states that give rise to entanglement entropy dominated by a term proportional to the area of the entangling surface.