Quantum Chaos, Delocalization, and Entanglement in Disordered Heisenberg Models

We investigate disordered one- and two-dimensional Heisenberg spin lattices across a transition from integrability to quantum chaos from both a statistical many-body and a quantum-information perspective. Special emphasis is devoted to quantitatively exploring the interplay between eigenvector statistics, delocalization, and entanglement in the presence of nontrivial symmetries. The implications of basis dependence of state delocalization indicators (such as the number of principal components) is addressed, and a measure of {\em relative delocalization} is proposed in order to robustly characterize the onset of chaos in the presence of disorder. Both standard multipartite and {\em generalized entanglement} are investigated in a wide parameter regime by using a family of spin- and fermion- purity measures, their dependence on delocalization and on energy spectrum statistics being examined. A distinctive {\em correlation between entanglement, delocalization, and integrability} is uncovered, which may be generic to systems described by the two-body random ensemble and may point to a new diagnostic tool for quantum chaos. Analytical estimates for typical entanglement of random pure states restricted to a proper subspace of the full Hilbert space are also established and compared with random matrix theory predictions.Comment: 17 pages, 10 figures, revised versio

Nested entangled states for distributed quantum channels

We find a coupling-strength configuration for a linear chain of N spins which gives rise to simultaneous multiple Bell states. We suggest a way such an interesting entanglement pattern can be used in order to distribute maximally entangled channels to remote locations and generate multipartite entanglement with a minimum-control approach. Our proposal thus provides a way to achieve the core resources in distributed information processing. The schemes we describe can be efficiently tested in chains of coupled cavities interacting with three-level atoms.Comment: 4 pages, 2 figures, RevTeX

Statistics of leading digits leads to unification of quantum correlations

We show that the frequency distribution of the first significant digits of the numbers in the data sets generated from a large class of measures of quantum correlations, which are either entanglement measures, or belong to the information-theoretic paradigm, exhibit a universal behaviour. In particular, for Haar uniformly simulated arbitrary two-qubit states, we find that the first-digit distribution corresponding to a collection of chosen computable quantum correlation quantifiers tend to follow the first-digit law, known as the Benford's law, when the rank of the states increases. Considering a two-qubit state which is obtained from a system governed by paradigmatic spin Hamiltonians, namely, the XY model in a transverse field, and the XXZ model, we show that entanglement as well as information theoretic measures violate the Benford's law. We quantitatively discuss the violation of the Benford's law by using a violation parameter, and demonstrate that the violation parameter can signal quantum phase transitions occurring in these models. We also comment on the universality of the statistics of first significant digits corresponding to appropriate measures of quantum correlations in the case of multipartite systems as well as systems in higher dimensions.Comment: v1: 11 pages, 5 figures, 2 tables; v2: 11 pages, 6 figures, 2 tables, new results added, extended version of the published pape