Multipartite Entanglement Signature of Quantum Phase Transitions

We derive a general relation between the non-analyticities of the ground state energy and those of a subclass of the multipartite generalized global entanglement (GGE) measure defined by T. R. de Oliveira et al. [Phys. Rev. A 73, 010305(R) (2006)] for many-particle systems. We show that GGE signals both a critical point location and the order of a quantum phase transition (QPT). We also show that GGE allows us to study the relation between multipartite entanglement and QPTs, suggesting that multipartite but not bipartite entanglement is favored at the critical point. Finally, using GGE we were able, at a second order QPT, to define a diverging entanglement length (EL) in terms of the usual correlation length. We exemplify this with the XY spin-1/2 chain and show that the EL is half the correlation length.Comment: Published version. Incorporates correction made in erratu

Genuine Multipartite Entanglement in Quantum Phase Transitions

We demonstrate that the Global Entanglement (GE) measure defined by Meyer and Wallach, J. Math. Phys. 43, 4273 (2002), is maximal at the critical point for the Ising chain in a transverse magnetic field. Our analysis is based on the equivalence of GE to the averaged linear entropy, allowing the understanding of multipartite entanglement (ME) features through a generalization of GE for bipartite blocks of qubits. Moreover, in contrast to GE, the proposed ME measure can distinguish three paradigmatic entangled states: $GHZ_{N}$, $W_{N}$, and $EPR^{\otimes N/2}$. As such the generalized measure can detect genuine ME and is maximal at the critical point.Comment: 4 pages, 3 figures. Replaced with final published versio

Strong superadditivity and monogamy of the Renyi measure of entanglement

Employing the quantum R\'enyi $\alpha$-entropies as a measure of entanglement, we numerically find the violation of the strong superadditivity inequality for a system composed of four qubits and $\alpha>1$. This violation gets smaller as $\alpha\rightarrow 1$ and vanishes for $\alpha=1$ when the measure corresponds to the Entanglement of Formation (EoF). We show that the R\'enyi measure aways satisfies the standard monogamy of entanglement for $\alpha = 2$, and only violates a high order monogamy inequality, in the rare cases in which the strong superadditivity is also violated. The sates numerically found where the violation occurs have special symmetries where both inequalities are equivalent. We also show that every measure satisfing monogamy for high dimensional systems also satisfies the strong superadditivity inequality. For the case of R\'enyi measure, we provide strong numerical evidences that these two properties are equivalent.Comment: replaced with final published versio

Operational Classification and Quantification of Multipartite Entangled States

We formalize and extend an operational multipartite entanglement measure introduced by T. R. Oliveira, G. Rigolin, and M. C. de Oliveira, Phys. Rev. A 73, 010305(R) (2006), through the generalization of global entanglement (GE) [D. A. Meyer and N. R. Wallach, J. Math. Phys. 43, 4273 (2002)]. Contrarily to GE the main feature of this measure lies in the fact that we study the mean linear entropy of all possible partitions of a multipartite system. This allows the construction of an operational multipartite entanglement measure which is able to distinguish among different multipartite entangled states that GE failed to discriminate. Furthermore, it is also maximum at the critical point of the Ising chain in a transverse magnetic field, being thus able to detect a quantum phase transition.Comment: 14 pages, RevTex4, published versio

Exotic looped trajectories via quantum marking

We provide an analytical and theoretical study of exotic looped trajectories (ELTs) in a double-slit interferometer with quantum marking. We use an excited Rydberg-like atom and which-way detectors such as superconducting cavities, just as in the Scully-Englert-Walther interferometer. We indicate appropriate conditions on the atomic beam or superconducting cavities so that we determine an interference pattern and fringe visibility exclusive from the ELTs. We quantitatively describe our results for Rubidium atoms and propose this framework as an alternative scheme to the double-slit experiment modified to interfere only these exotic trajectories.Comment: 10 pages, 5 figure

Symmetry breaking effects upon bipartite and multipartite entanglement in the XY model

We analyze the bipartite and multipartite entanglement for the ground state of the one-dimensional XY model in a transverse magnetic field in the thermodynamical limit. We explicitly take into account the spontaneous symmetry breaking in order to explore the relation between entanglement and quantum phase transitions. As a result we show that while both bipartite and multipartite entanglement can be enhanced by spontaneous symmetry breaking deep into the ferromagnetic phase, only the latter is affected by it in the vicinity of the critical point. This result adds to the evidence that multipartite, and not bipartite, entanglement is the fundamental indicator of long range correlations in quantum phase transitions.Comment: 13 pages, 19 figures, comments welcome. V2: small changes, published versio

Macroinvertebrates associated with bryophyta in a first-order Atlantic Forest stream

This study describes the composition and structure of the benthic community associated with bryophytes in a first-order stream, located in a biological reserve of the Atlantic Forest, during two seasons. During three months of the dry season of 2007 and three months of the rainy season of 2008, samples of bryophytes attached to stones were collected randomly, along a 100 m stream reach. The structure of the community was analyzed through the mean density of individuals, Shannon's diversity index, Pielou's evenness, family richness, dominance index, and the percentage of Ephemeroptera, Plecoptera and Trichoptera (% EPT). Chironomidae larvae were dominant in the two periods of study, followed by Ceratopogonidae in the rainy season, and Naididae in the dry season. The orders EPT contributed 14 families. The results showed that bryophytes constitute suitable habitat which is able to shelter an abundant and diversified benthic fauna in a small extension of the stream. This habitat provides refuge during spates, and thus minimizes downstream transport of the macroinvertebrate fauna.