Continuous-discrete entanglement: an example with non-relativistic particles

Abstract

This article discusses entanglement between two subsystems, one with discrete degrees of freedom and the other with continuous degrees of freedom. The overlap integral between continuous variable wave functions emerges as an important parameter to characterize this kind entanglement. ``Beam-like'' entanglement and ``shape-like'' entanglement are contrasted. One example of this kind of entanglement is between between the spin degrees of freedom and the momentum degrees of freedom for a non-relativistic particle. This intraparticle entanglement is Galilean invariant.