  The controlled generation and identification of quantum correlations, usually
encoded in either qubits or continuous degrees of freedom, builds the
foundation of quantum information science. Recently, more sophisticated
approaches, involving a combination of two distinct degrees of freedom have
been proposed to improve on the traditional strategies. Hyperentanglement
describes simultaneous entanglement in more than one distinct degree of
freedom, whereas hybrid entanglement refers to entanglement shared between a
discrete and a continuous degree of freedom. In this work we propose a scheme
that allows to combine the two approaches, and to extend them to the strongest
form of quantum correlations. Specifically, we show how two identical,
initially separated particles can be manipulated to produce Bell nonlocality
among their spins, among their momenta, as well as across their spins and
momenta. We discuss possible experimental realizations with atomic and photonic
systems.
