  We introduce a generalization of entanglement based on the idea that
entanglement is relative to a distinguished subspace of observables rather than
a distinguished subsystem decomposition. A pure quantum state is entangled
relative to such a subspace if its expectations are a proper mixture of those
of other states. Many information-theoretic aspects of entanglement can be
extended to the general setting, suggesting new ways of measuring and
classifying entanglement in multipartite systems. By going beyond the
distinguishable-subsystem framework, generalized entanglement also provides
novel tools for probing quantum correlations in interacting many-body systems.
