A subsystem-independent generalization of entanglement

Abstract

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.

5 pages, 1 encapsulated color figure, REVTeX4 style

References in corpus (3)

• Entanglement in quantum critical phenomena
• Generalizations of entanglement based on coherent states and convex sets
• Unveiling Order behind Complexity: Coexistence of Ferromagnetism and Bose-Einstein Condensation

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