A subsystem-independent generalization of entanglement

TLDR: In this article, a generalization of entanglement based on the notion of a distinguished subspace of observables rather than a distinguished subsystem decomposition is presented. But it does not address how to measure and classify multipartite entanglements.

Abstract: We present 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 this observable-based setting, suggesting new ways of measuring and classifying multipartite entanglement. By going beyond the distinguishable-subsystem framework, generalized entanglement also provides novel tools for probing quantum correlations in interacting many-body systems.