Tripartite Entanglement versus Tripartite Nonlocality in Three-Qubit Greenberger-Horne-Zeilinger-Class States

We analyze the relationship between tripartite entanglement and genuine tripartite nonlocality for three-qubit pure states in the Greenberger-Horne-Zeilinger class. We consider a family of states known as the generalized Greenberger-Horne-Zeilinger states and derive an analytical expression relating the three-tangle, which quantifies tripartite entanglement, to the Svetlichny inequality, which is a Bell-type inequality that is violated only when all three qubits are nonlocally correlated. We show that states with three-tangle less than 1/2 do not violate the Svetlichny inequality. On the other hand, a set of states known as the maximal slice states does violate the Svetlichny inequality, and exactly analogous to the two-qubit case, the amount of violation is directly related to the degree of tripartite entanglement. We discuss further interesting properties of the generalized Greenberger-Horne-Zeilinger and maximal slice states.

Svetlichny's inequality and genuine tripartite nonlocality in three-qubit pure states

The violation of the Svetlichny's inequality (SI) [Phys. Rev. D 35, 3066 (1987)] is sufficient but not necessary for genuine tripartite nonlocal correlations. Here we quantify the relationship between tripartite entanglement and the maximum expectation value of the Svetlichny operator (which is bounded from above by the inequality) for the two inequivalent subclasses of pure three-qubit states: the Greenberger-Horne-Zeilinger (GHZ) class and the W class. We show that the maximum for the GHZ-class states reduces to Mermin's inequality [Phys. Rev. Lett. 65, 1838 (1990)] modulo a constant factor, and although it is a function of the three tangle and the residual concurrence, large numbers of states do not violate the inequality. We further show that by design SI is more suitable as a measure of genuine tripartite nonlocality between the three qubits in the W-class states,and the maximum is a certain function of the bipartite entanglement (the concurrence) of the three reduced states, and only when their sum attains a certain threshold value do they violate the inequality.

Optimal values of bipartite entanglement in a tripartite system

For a general tripartite system in some pure state, an observer possessing any two parts will see them in a mixed state. By the consequence of Hughston-Jozsa-Wootters theorem, each basis set of local measurement on the third part will correspond to a particular decomposition of the bipartite mixed state into a weighted sum of pure states. It is possible to associate an average bipartite entanglement ((S) over bar) with each of these decompositions. The maximum value of (S) over bar is called the entanglement of assistance (E-A) while the minimum value is called the entanglement of formation (E-F). An appropriate choice of the basis set of local measurement will correspond to an optimal value of (S) over bar; we find here a generic optimality condition for the choice of the basis set. In the present context, we analyze the tripartite states W and GHZ and show how they are fundamentally different. (C) 2014 Elsevier B.V. All rights reserved.

Social evolution - Has nature ever rewound the tape?

Social insects such as ants, bees, wasps and termites exhibit extreme forms of altruism where some individuals remain sterile and assist other individuals in reproduction. Hamilton's inclusive fitness theory provides a powerful framework for investigating the evolution of such altruism. Using the paper wasp Ropalidia marginata, we have quantified and delineated the role of ecological, physiological, genetic and demographic factors in social evolution. An interesting feature of the models we have developed is their symmetry so that either altruism or selfishness can evolve, depending on the numerical values of various parameters. This suggests that selfish/solitary behaviour must occasionally re-emerge even from the eusocial state, It is useful to contemplate expected intermediate states during such potential reversals. We can perhaps envisage three successive steps in such a hypothetical process: i) workers revolt against the hegemony of the queen and challenge her status as the sole reproductive, ii) workers stop producing queens and one or more of them function as egg layers (functional queen/s) capable of producing both haploid as well as diploid offspring and iii) social evolution reverses completely so that a eusocial species becomes solitary, at least facultatively. It appears that the third step, namely transition from eusociality to the solitary state, is rare and has been restricted to transitions from the primitively eusocial state only. The absence of transitions from the highly eusocial state to the solitary state may be attributed to a number of 'preventing mechanisms' such as (a) queen control of workers (b) loss of spermathecae and ability to mate (c) morphological specialization (d) caste polyethism and (e) homeostasis, which must each make the transition difficult and, taken together, perhaps very difficult. However, the discovery of a transition from the highly eusocial to the solitary state can hardly he ruled out, given that little or no effort has gone into its detection. In this paper I discuss social evolution and its possible reversal and cite potential examples of stages in the transition from the social to the solitary.

Phosphorylation status of the phosphoprotein P of rinderpest virus modulates transcription and replication of the genome

The phosphoprotein P of paramyxoviruses is known to play more than one role in genome transcription and replication. Phosphorylation of P at the NH2 terminus by cellular casein kinase II has been shown to be necessary for transcription of the genome in some of the viruses, while it is dispensable for replication. The phosphorylation null mutant of rinderpest virus P protein, in which three serine residues have been mutated, has been shown earlier to be non-functional in an in vivo minigenome replication/transcription system. In this work, we have shown that the phosphorylation of P protein is essential for transcription, whereas the null mutant is active in replication of the genome in vivo. The null mutant P acts as a transdominant repressor of transcriptional activity of wild-type P and as an activator of replication carried out by wild-type P protein. These results suggest the phosphorylation status of P may act as a replication switch during virus replication. We also show that the phosphorylation null mutant P is capable of interacting with L and N proteins and is able to form a tripartite complex of L-(N-P) when expressed in insect cells, similar to wild-type P protein.

Genetic Heterogeneity in Wild Isolates of Cellular Slime Mold Social Groups

This study addresses the issues of spatial distribution, dispersal, and genetic heterogeneity in social groups of the cellular slime molds (CSMs). The CSMs are soil amoebae with an unusual life cycle that consists of alternating solitary and social phases. Because the social phase involves division of labor with what appears to be an extreme form of "altruism", the CSMs raise interesting evolutionary questions regarding the origin and maintenance of sociality. Knowledge of the genetic structure of social groups in the wild is necessary for answering these questions. We confirm that CSMs are widespread in undisturbed forest soil from South India. They are dispersed over long distances via the dung of a variety of large mammals. Consistent with this mode of dispersal, most social groups in the two species examined for detailed study, Dictyostelium giganteum and Dictyostelium purpureum, are multi-clonal.

Sociobiology in turmoil again

Altruism is defined as any behaviour that lowers the Darwinian fitness of the actor while increasing that of the recipient. Such altruism (especially in the form of lifetime sterility exhibited by sterile workers in eusocial insects such as ants, bees, wasps and termites) has long been considered a major difficulty for the theory of natural selection. In the 1960s W. D. Hamilton potentially solved this problem by defining a new measure of fitness that he called inclusive fitness, which also included the effect of an individual's action on the fitness of genetic relatives. This has come to be known as inclusive fitness theory, Hamilton's rule or kin selection. E. O. Wilson almost single-handedly popularized this new approach in the 1970s and thus helped create a large body of new empirical research and a large community of behavioural ecologists and kin selectionists. Adding thrill and drama to our otherwise sombre lives, Wilson is now leading a frontal attack on Hamilton's approach, claiming that the inclusive fitness theory is not as mathematically general as the standard natural selection theory, has led to no additional biological insights and should therefore be abandoned. The world cannot but sit up and take notice.

Entanglement and nonclassicality for multimode radiation-field states

Nonclassicality in the sense of quantum optics is a prerequisite for entanglement in multimode radiation states. In this work we bring out the possibilities of passing from the former to the latter, via action of classicality preserving systems like beam splitters, in a transparent manner. For single-mode states, a complete description of nonclassicality is available via the classical theory of moments, as a set of necessary and sufficient conditions on the photon number distribution. We show that when the mode is coupled to an ancilla in any coherent state, and the system is then acted upon by a beam splitter, these conditions turn exactly into signatures of negativity under partial transpose (NPT) entanglement of the output state. Since the classical moment problem does not generalize to two or more modes, we turn in these cases to other familiar sufficient but not necessary conditions for nonclassicality, namely the Mandel parameter criterion and its extensions. We generalize the Mandel matrix from one-mode states to the two-mode situation, leading to a natural classification of states with varying levels of nonclassicality. For two-mode states we present a single test that can, if successful, simultaneously show nonclassicality as well as NPT entanglement. We also develop a test for NPT entanglement after beam-splitter action on a nonclassical state, tracing carefully the way in which it goes beyond the Mandel nonclassicality test. The result of three-mode beam-splitter action after coupling to an ancilla in the ground state is treated in the same spirit. The concept of genuine tripartite entanglement, and scalar measures of nonclassicality at the Mandel level for two-mode systems, are discussed. Numerous examples illustrating all these concepts are presented.

Social selection and the evolution of cooperative groups: The example of the cellular slime moulds

In social selection the phenotype of an individual depends on its own genotype as well as on the phenotypes, and so genotypes, of other individuals. This makes it impossible to associate an invariant phenotype with a genotype: the social context is crucial. Descriptions of metazoan development, which often is viewed as the acme of cooperative social behaviour, ignore or downplay this fact. The implicit justification for doing so is based on a group-selectionist point of view. Namely, embryos are clones, therefore all cells have the same evolutionary interest, and the visible differences between cells result from a common strategy. The reasoning is flawed, because phenotypic heterogeneity within groups can result from contingent choices made by cells from a flexible repertoire as in multicellular development. What makes that possible is phenotypic plasticity, namely the ability of a genotype to exhibit different phenotypes. However, co-operative social behaviour with division of labour requires that different phenotypes interact appropriately, not that they belong to the same genotype, or have overlapping genetic interests. We sketch a possible route to the evolution of social groups that involves many steps: (a) individuals that happen to be in spatial proximity benefit simply by virtue of their number; (b) traits that are already present act as preadaptations and improve the efficiency of the group; and (c) new adaptations evolve under selection in the social context-that is, via interactions between individuals-and further strengthen group behaviour. The Dictyostelid or cellular slime mould amoebae (CSMs) become multicellular in an unusual way, by the aggregation of free-living cells. In nature the resulting group can be genetically homogeneous (clonal) or heterogeneous (polyclonal); in either case its development, which displays strong cooperation between cells (to the extent of so-called altruism) is not affected. This makes the CSMs exemplars for the study of social behaviour.

Why the Definition of Eusociality Is Not Helpful to Understand Its Evolution and What Should We Do about It

The evolution of altruism is the central problem of the evolution of eusociality. The evolution of altruism is most likely to be understood by studying species that show altruism in spite of being capable of ''selfish'' individual reproduction. But the definition of eusociality groups together primitively eusocial species where workers retain the ability to reproduce on their own and highly eusocial species where workers have lost reproductive options. At the same time it separates the primitively eusocial species from semisocial species, species that lack life-time sterility and cooperatively breeding birds and mammals, in most of which, altruism and the associated social life are facultative. The definition of eusociality is also such that it is sometimes difficult to decide,what is eusocial and what is not. I therefore suggest that, (1) we expand the scope of eusociality to include semisocial species, primitively eusocial species, highly eusocial species as well as those cooperatively breeding birds and mammals where individuals give up substantial or all personal reproduction for aiding conspecifics, (2) there should be no requirement of overlap of generations or of life-time sterility and (3) the distinction between primitively and highly eusocial should continue, based on the presence or absence of morphological caste differentiation.

A profile of adenosine triphosphate

An attempt is made to draw a profile of adenosine triphosphate (ATP) and to project its many actions. The amazing versatility of its participation in a number of synthetic reactions lies in the oligophosphate structure. Many proteins that use ATP have conserved binding 'P-loop' but this gives no clue what makes it so special. The energy transducing reactions leading to synthesis of the terminal phosphodiester had at least three strategies. Of these, direct dehydration and transfer of inorganic phosphate using respiratory energy operate through mechano-coupling in a multisubunit protein. This tripartite, knob-stalk-base structure provides a novel mechanism of rotational catalysis and the tiniest molecular motor, All the reactions occur in concert with no sign of energized chemical intermediate. With the new knowledge on the crystal structure of F-1-ATPase, proton translocation needs a relook. An alternative perspective is emerging on energy being received and stored in polypeptide structure by breaking hydrogen bonds. Membrane serves the purpose of mobilizing the constituent proteins and also as a potential energy carrier of proteins with little loss of energy.

Altruistic Wasps?

Polistes dominulus is one of the most common social wasps in Europe and is an invasive species in the United States. Its wide prevalence has made it one of the best-studied social wasps. In most social wasps, the female wasps live in a colony and organize themselves into a behavioral dominance hierarchy such that only the dominant alpha individual (the queen) reproduces while the rest function as apparently altruistic, sterile subordinates (workers), building the nest, foraging for food and pulp, and feeding and caring for the brood. Why should workers invest their time and energy helping to rear the queen's brood, rather than found their own nests and rear their own brood—something they are quite capable of? On page 874 of this issue, Leadbeater et al. (1) show that the subordinates indeed produce their own offspring and this raises interesting questions about the links between altruism, direct reproduction, and the evolution of social behavior.

Males, but not females, mate with multiple partners: a laboratory study of a primitively eusocial wasp Ropalidia marginata

The intense interest in social Hymenoptera, on account of their elaborate sociality and the paradox of altruism, has often suffered from considerable gender imbalance. This is partly due to the fact that worker behaviour and altruism are restricted to the females and partly because males often live off the nest. Yet, understanding the males, especially in the context of mating biology is essential even for understanding the evolution of sociality. Mating patterns have a direct bearing on the levels of intra-colony genetic relatedness, which in turn, along with the associated costs and benefits of worker behaviour, are central to our understanding of the evolution of sociality. Although mating takes place away from the nest in natural colonies of the primitively eusocial wasp Ropalidia marginata, mating can be observed in the laboratory if a male and a female are placed in a transparent, aerated plastic container, and both wasps are in the range of 5-20 days of age. Here, we use this setup and show that males, but not females, mate serially with multiple partners. The multiple mating behaviour of the males is not surprising because in nature males have to mate with a number of females, only a few of whom will go on to lay eggs. The reluctance of R. marginata females to mate with multiple partners is consistent with the expectation of monogamy in primitively eusocial species with totipotent females, although the apparent discrepancy with a previous work with allozyme markers in natural colonies suggesting that females may sometimes mate with two or three different males remains to be resolved.

The N-terminal region containing the zinc finger domain of tobacco streak virus coat protein is essential for the formation of virus-like particles

Tobacco streak virus (TSV), a member of the genus Ilarvirus (family Bromoviridae), has a tripartite genome and forms quasi-isometric virions. All three viral capsids, encapsidating RNA 1, RNA 2 or RNA 3 and subgenomic RNA 4, are constituted of a single species of coat protein (CP). Formation of virus-like particles (VLPs) could be observed when the TSV CP gene was cloned and the recombinant CP (rCP) was expressed in E. coli. TSV VLPs were found to be stabilized by Zn2+ ions and could be disassembled in the presence of 500 mM CaCl2. Mutational analysis corroborated previous studies that showed that an N-terminal arginine-rich motif was crucial for RNA binding; however, the results presented here demonstrate that the presence of RNA is not a prerequisite for assembly of TSV VLPs. Instead, the N-terminal region containing the zinc finger domain preceding the arginine-rich motif is essential for assembly of these VLPs.

Counterfactual quantum certificate authorization

We present a multipartite protocol in a counterfactual paradigm. In counterfactual quantum cryptography, secure information is transmitted between two spatially separated parties even when there is no physical travel of particles transferring the information between them. We propose here a tripartite counterfactual quantum protocol for the task of certificate authorization. Here a trusted third party, Alice, authenticates an entity Bob (e.g., a bank) that a client Charlie wishes to securely transact with. The protocol is counterfactual with respect to either Bob or Charlie. We prove its security against a general incoherent attack, where Eve attacks single particles.