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arXiv:1310.3089 · International Journal of Quantum Information

Entanglement entropy in quasi-symmetric multi-qubit states

Zhihua Li, An Min Wang

Published Feb 24, 2015• 10 citations
arXivHTMLPDF

Abstract

We generalize the symmetric multi-qubit states to their q-analogs, whose basis vectors are identified with the q-Dicke states. We study the entanglement entropy in these states and find that entanglement is extruded towards certain regions of the system due to the inhomogeneity aroused by q-deformation. We also calculate entanglement entropy in ground states of a related q-deformed Lipkin–Meshkov–Glick (LMG) model and show that the singularities of entanglement can correctly signify the quantum phase transition points for different strengths of q-deformation.

DOI
10.1142/s0219749915500070

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Abstract We introduce a new class of generalized isotropic Lipkin–Meshkov–Glick models with spin and long-range non-constant interactions, whose non-degenerate ground state is a Dicke state of type. We evaluate in closed form the reduced density matrix of a block of L spins when the whole system is in its ground state, and study the corresponding von Neumann and Rényi entanglement entropies in the thermodynamic limit. We show that both of these entropies scale as when L tends to infinity, where the coefficient a is equal to ( m − k )/2 in the ground state phase with k vanishing magnon densities. In particular, our results show that none of these generalized Lipkin–Meshkov–Glick models are critical, since when their Rényi entropy R q becomes independent of the parameter q . We have also computed the Tsallis entanglement entropy of the ground state of these generalized Lipkin–Meshkov–Glick models, finding that it can be made extensive by an appropriate choice of its parameter only when . Finally, in the case we construct in detail the phase diagram of the ground state in parameter space, showing that it is determined in a simple way by the weights of the fundamental representation of . This is also true in the case; for instance, we prove that the region for which all the magnon densities are non-vanishing is an ( m + 1)-simplex in whose vertices are the weights of the fundamental representation of .
Abstract Collective spin operators for symmetric multi-quDit (namely identical D -level atom) systems generate a U( D ) symmetry. We explore generalizations to arbitrary D of SU(2)-spin coherent states and their adaptation to parity (multi-component Schrödinger cats), together with multi-mode extensions of NOON states. We write level, one- and two-quDit reduced density matrices of symmetric N -quDit states, expressed in the last two cases in terms of collective U( D )-spin operator expectation values. Then, we evaluate level and particle entanglement for symmetric multi-quDit states with linear and von Neumann entropies of the corresponding reduced density matrices. In particular, we analyze the numerical and variational ground state of Lipkin–Meshkov–Glick models of 3-level identical atoms. We also propose an extension of the concept of SU(2)-spin squeezing to SU( D ) and relate it to pairwise D -level atom entanglement. Squeezing parameters and entanglement entropies are good markers that characterize the different quantum phases, and their corresponding critical points, that take place in these interacting D -level atom models.