  Entanglement, or quantum inseparability, is a crucial resource in quantum
information applications, and therefore the experimental generation of
separated yet entangled systems is of paramount importance. Experimental
demonstrations of inseparability with light are not uncommon, but such
demonstrations in physically well-separated massive systems, such as distinct
gases of atoms, are new and present significant challenges and opportunities.
Rigorous theoretical criteria are needed for demonstrating that given data are
sufficient to confirm entanglement. Such criteria for experimental data have
been derived for the case of continuous-variable systems obeying the
Heisenberg-Weyl (position- momentum) commutator. To address the question of
experimental verification more generally, we develop a sufficiency criterion
for arbitrary states of two arbitrary systems. When applied to the recent study
by Julsgaard, Kozhekin, and Polzik [Nature 413, 400 - 403 (2001)] of spin-state
entanglement of two separate, macroscopic samples of atoms, our new criterion
confirms the presence of spin entanglement.
