Anticoherence measures for pure spin states

The set of pure spin states with vanishing spin expectation value can be regarded as the set of the less coherent pure spin states. This set can be divided into a finite number of nested subsets on the basis of higher order moments of the spin operators. This subdivision relies on the notion of anticoherent spin state to order $t$: A spin state is said to be anticoherent to order $t$ if the moment of order $k$ of the spin components along any directions are equal for $k= 1, 2,\ldots, t$. Most spin states are neither coherent nor anticoherent, but can be arbitrary close to one or the other. In order to quantify the degree of anticoherence of pure spin states, we introduce the notion of anticoherence measures. By relying on the mapping between spin-$j$ states and symmetric states of $2j$ spin-$1/2$ (Majorana representation), we present a systematic way of constructing anticoherence measures to any order. We briefly discuss their connection with measures of quantum coherence. Finally, we illustrate our measures on various spin states and use them to investigate the problem of the existence of anticoherent spin states with degenerated Majorana points

Multiqubit symmetric states with maximally mixed one-qubit reductions

We present a comprehensive study of maximally entangled symmetric states of arbitrary numbers of qubits in the sense of the maximal mixedness of the one-qubit reduced density operator. A general criterion is provided to easily identify whether given symmetric states are maximally entangled in that respect or not. We show that these maximally entangled symmetric (MES) states are the only symmetric states for which the expectation value of the associated collective spin of the system vanishes, as well as in corollary the dipole moment of the Husimi function. We establish the link between this kind of maximal entanglement, the anticoherence properties of spin states, and the degree of polarization of light fields. We analyze the relationship between the MES states and the classes of states equivalent through stochastic local operations with classical communication (SLOCC). We provide a nonexistence criterion of MES states within SLOCC classes of qubit states and show in particular that the symmetric Dicke state SLOCC classes never contain such MES states, with the only exception of the balanced Dicke state class for even numbers of qubits. The 4-qubit system is analyzed exhaustively and all MES states of this system are identified and characterized. Finally the entanglement content of MES states is analyzed with respect to the geometric and barycentric measures of entanglement, as well as to the generalized N-tangle. We show that the geometric entanglement of MES states is ensured to be larger than or equal to 1/2, but also that MES states are not in general the symmetric states that maximize the investigated entanglement measures.Comment: 12 pages, 4 figure

Anticoherence of spin states with point group symmetries

We investigate multiqubit permutation-symmetric states with maximal entropy of entanglement. Such states can be viewed as particular spin states, namely anticoherent spin states. Using the Majorana representation of spin states in terms of points on the unit sphere, we analyze the consequences of a point-group symmetry in their arrangement on the quantum properties of the corresponding state. We focus on the identification of anticoherent states (for which all reduced density matrices in the symmetric subspace are maximally mixed) associated with point-group symmetric sets of points. We provide three different characterizations of anticoherence, and establish a link between point symmetries, anticoherence and classes of states equivalent through stochastic local operations with classical communication (SLOCC). We then investigate in detail the case of small numbers of qubits, and construct infinite families of anticoherent states with point-group symmetry of their Majorana points, showing that anticoherent states do exist to arbitrary order.Comment: 15 pages, 5 figure

Tensor Representation of Spin States

We propose a generalization of the Bloch sphere representation for arbitrary spin states. It provides a compact and elegant representation of spin density matrices in terms of tensors that share the most important properties of Bloch vectors. Our representation, based on covariant matrices introduced by Weinberg in the context of quantum field theory, allows for a simple parametrization of coherent spin states, and a straightforward transformation of density matrices under local unitary and partial tracing operations. It enables us to provide a criterion for anticoherence, relevant in a broader context such as quantum polarization of light.Comment: 5 pages + 7 pages of supplementary informatio

Metacommunity Dynamics: Decline of Functional Relationship along a Habitat Fragmentation Gradient

Background: The metacommunity framework is crucial to the study of functional relations along environmental gradients. Changes in resource grain associated with increasing habitat fragmentation should generate uncoupled responses of interacting species with contrasted dispersal abilities. Methodology/Principal Findings: Here we tested whether the intensity of parasitism was modified by increasing habitat fragmentation in the well know predator-prey system linking the parasitoid Cotesia glomerata (Hymenoptera: Braconidae) to its main host Pieris brassicae (Lepidoptera: Pieridae). We collected information on herbivorous abundance and parasitism rate along an urbanization gradient from the periphery to the centre of Paris. We showed that butterfly densities were not influenced by habitat fragmentation, whereas parasitism rate sharply decreased along this gradient. Conclusions/Significance: Our results provide novel insights into the mechanisms underlying the persistence of species in highly fragmented areas. They suggest that differential dispersal abilities could alter functional relationships between prey and predator, notably by a lack of natural predators

Selection on the wing in Heliconius butterflies

<p>Asbtract</p> <p>To what extent population structure favours the establishment of new phenotypes within a species remains a fundamental question in evolutionary studies. By reducing gene flow, habitat fragmentation is a major factor shaping the genetic structuring of populations, favouring isolation of small populations in which drift may rapidly change frequencies of new variants. When these variants provide advantages to individuals, the combined effect of selection and drift can lead to rapid shifts in phenotypes. In a study published in <it>BMC Genetics</it>, Albuquerque de Moura <it>et al. </it>asked whether such a general pattern of population structure can be observed in <it>Heliconius </it>species, which could have strong implication in the evolution of colour pattern diversification in these butterflies. In this commentary we discuss the potential roles of these three processes (drift, selection and dispersal) on the evolution of <it>Heliconius </it>wing patterns in regard to the findings of a common fine-scale population structure within the co-mimetic species <it>H. melpomene </it>and <it>H. erato</it>. Indeed, a general pattern of population subdivision in the history of these two species may have provoked the major phenotypical shifts observed in their wing colour patterns. The suggestion that coupled environmental pressures (counter-selection of dispersal and selection on co-evolved traits) could be responsible for identical genetic differentiation profiles in <it>H. erato </it>and <it>H. melpomene </it>clearly merits further investigations using both detailed population genetic (including landscape genetic) and ecological studies.</p

Gene flow rise with habitat fragmentation in the bog fritillary butterfly (Lepidoptera: Nymphalidae)

<p>Abstract</p> <p>Background</p> <p>The main components of the spatial genetic structure of the populations are neighbourhood size and isolation by distance. These may be inferred from the allele frequencies across a series of populations within a region. Here, the spatial population structure of <it>Proclossiana eunomia </it>was investigated in two mountainous areas of southern Europe (Asturias, Spain and Pyrenees, France) and in two areas of intermediate elevation (Morvan, France and Ardennes, Belgium).</p> <p>Results</p> <p>A total of eight polymorphic loci were scored by allozyme electrophoresis, revealing a higher polymorphism in the populations of southern Europe than in those of central Europe.</p> <p>Isolation by distance effect was much stronger in the two mountain ranges (Pyrenees and Asturias) than in the two areas of lower elevation (Ardennes and Morvan). By contrast, the neighbourhood size estimates were smaller in the Ardennes and in the Morvan than in the two high mountain areas, indicating more common movements between neighbouring patches in the mountains than in plains.</p> <p>Conclusion</p> <p>Short and long dispersal events are two phenomena with distinct consequences in the population genetics of natural populations. The differences in level of population differentiation within each the four regions may be explained by change in dispersal in lowland recently fragmented landscapes: on average, butterflies disperse to a shorter distance but the few ones which disperse long distance do so more efficiently. Habitat fragmentation has evolutionary consequences exceeding by far the selection of dispersal related traits: the balance between local specialisation and gene flow would be perturbed, which would modify the extent to which populations are adapted to heterogeneous environments.</p

Quantitative analysis of changes in movement behaviour within and outside habitat in a specialist butterfly

BACKGROUND: Dispersal between habitat patches is a key process in the functioning of (meta)populations. As distance between suitable habitats increases, the ongoing process of habitat fragmentation is expected to generate strong selection pressures on movement behaviour. This leads to an increase or decrease of dispersal according to its cost relative to landscape structure. To limit the cost of dispersal in an increasingly hostile matrix, we predict that organisms would adopt special dispersal behaviour between habitats, which are different from movements associated with resource searching in suitable habitats. RESULTS: Here we quantified the movement behaviour of the bog fritillary butterfly (Proclossiana eunomia) by (1) assessing perceptual range, the distance to which the habitat can be perceived, and (2) tracking and parameterizing movement behaviour within and outside habitat (parameters were move length and turning angles distributions). Results are three-fold. (1) Perceptual range was < 30 m. (2) Movements were significantly straighter in the matrix than within the habitat. (3) Correlated random walk adequately described movement behaviour for 70% of the observed movement paths within habitat and in the matrix. CONCLUSION: The perceptual range being lower than the distance between habitat patches in the study area, P. eunomia likely perceives these habitat networks as fragmented, and must locate suitable habitats while dispersing across the landscape matrix. Such a constraint means that dispersal entails costs, and that selection pressure should favour behaviours that limit these costs. Indeed, our finding that dispersal movements in the matrix are straighter than resource searching movements within habitat supports the prediction of simulation studies that adopting straight movements for dispersal reduces its costs in fragmented landscapes. Our results support the mounting evidence that dispersal in fragmented landscapes evolved towards the use of specific movement behaviour, different from explorative searching movements within habitat

Effects of individual and population parameters on reproductive success in three sexually deceptive orchid species

Reproductive success (RS) in orchids in general, and in non-rewarding species specifically, is extremely low. RS is pollinator and pollination limited in food deceptive orchids, but this has rarely been studied in sexually deceptive orchid species. Here, we tested the effects of several individual (plant height, inflorescence size, nearest neighbour distance and flower position) and population (patch geometry, population density and size) parameters on RS in three sexually deceptive Ophrys (Orchidaceae) species. Inter-specific differences were observed in RS of flowers situated in the upper versus the lower part of the inflorescence, likely due to species-specific pollinator behaviour. For all three species examined, RS increased with increasing plant height, inflorescence size and nearest neighbour distance. RS generally increased with decreasing population density and increasing patch elongation. Given these results, we postulate that pollinator availability, rather than pollinator learning, is the most limiting factor in successful reproduction for sexually deceptive orchids. Our results also suggest that olfactory ‘display’ (i.e. versus optical display), in terms of inflorescence size (and covarying plant height), plays a key role in individual RS of sexually deceptive orchids. In this regard, several hypotheses are suggested and discusse

A stochastic movement simulator improves estimates of landscape connectivity

Acknowledgments This publication issued from the project TenLamas funded by the French Ministère de l'Energie, de l'Ecologie, du Développement Durable et de la Mer through the EU FP6 BiodivERsA Eranet; by the Agence Nationale de la Recherche (ANR) through the open call INDHET and 6th extinction MOBIGEN to V. M. Stevens, M. Baguette, and A. Coulon, and young researcher GEMS (ANR-13-JSV7-0010-01) to V. M. Stevens and M. Baguette; and by a VLIR-VLADOC scholarship awarded to J. Aben. L. Lens, J. Aben, D. Strubbe, and E. Matthysen are grateful to the Research Foundation Flanders (FWO) for financial support of fieldwork and genetic analysis (grant G.0308.13). V. M. Stevens and M. Baguette are members of the “Laboratoire d'Excellence” (LABEX) entitled TULIP (ANR-10-LABX-41). J. M. J. Travis and S. C. F. Palmer also acknowledge the support of NERC. A. Coulon and J. Aben contributed equally to the work.Peer reviewedPublisher PD