A Subsystem-Independent Generalization of Entanglement

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.

Figure 1

Analytic behavior of the (shifted) purity, $\underset{N\to \infty }{lim}{P}_{\mathfrak{u}(N)}^{\prime }$, for the BCS state as a function of $g$. It scales with an exponent $\nu =1$ near $g_c$ [20]. Thus, the correlation length diverges as $(g_c-g{)}^{-\nu }$ (Ising universality class).