Geometric Entanglement of Symmetric States and the Majorana Representation

Permutation-symmetric quantum states appear in a variety of physical situations, and they have been proposed for quantum information tasks. This article builds upon the results of [New J. Phys. 12, 073025 (2010)], where the maximally entangled symmetric states of up to twelve qubits were explored, and their amount of geometric entanglement determined by numeric and analytic means. For this the Majorana representation, a generalization of the Bloch sphere representation, can be employed to represent symmetric n qubit states by n points on the surface of a unit sphere. Symmetries of this point distribution simplify the determination of the entanglement, and enable the study of quantum states in novel ways. Here it is shown that the duality relationship of Platonic solids has a counterpart in the Majorana representation, and that in general maximally entangled symmetric states neither correspond to anticoherent spin states nor to spherical designs. The usability of symmetric states as resources for measurement-based quantum computing is also discussed.Comment: 10 pages, 8 figures; submitted to Lecture Notes in Computer Science (LNCS

Deliberation on Childhood Vaccination in Canada: Public Input on Ethical Trade-Offs in Vaccination Policy

Background: Policy decisions about childhood vaccination require consideration of multiple, sometimes conflicting, public health and ethical imperatives. Examples of these decisions are whether vaccination should be mandatory and, if so, whether to allow for non-medical exemptions. In this article we argue that these policy decisions go beyond typical public health mandates and therefore require democratic input. Methods: We report on the design, implementation, and results of a deliberative public forum convened over four days in Ontario, Canada, on the topic of childhood vaccination. Results: 25 participants completed all four days of deliberation and collectively developed 20 policy recommendations on issues relating to mandatory vaccinations and exemptions, communication about vaccines and vaccination, and AEFI (adverse events following immunization) compensation and reporting. Notable recommendations include unanimous support for mandatory childhood vaccination in Ontario, the need for broad educational communication about vaccination, and the development of a no-fault compensation scheme for AEFIs. There was persistent disagreement among deliberants about the form of exemptions from vaccination (conscience, religious beliefs) that should be permissible, as well as appropriate consequences if parents do not vaccinate their children. Conclusions: We conclude that conducting deliberative democratic processes on topics that are polarizing and controversial is viable and should be further developed and implemented to support democratically legitimate and trustworthy policy about childhood vaccination

The varved succession of Crawford Lake, Milton, Ontario, Canada as a candidate Global boundary Stratotype Section and Point for the Anthropocene series

An annually laminated succession in Crawford Lake, Ontario, Canada is proposed as the Global boundary Stratotype Section and Point (GSSP) for the Anthropocene as a series/epoch with a base dated at 1950 CE. Varve couplets of organic matter capped by calcite precipitated each summer in alkaline surface waters reflect environmental change at global to local scales. Spheroidal carbonaceous particles and nitrogen isotopes record an increase in fossil fuel combustion in the early 1950s, coinciding with fallout from nuclear and thermonuclear testing—239+240Pu and 14C:12C, the latter more than compensating for the effects of old carbon in this dolomitic basin. Rapid industrial expansion in the North American Great Lakes region led to enhanced leaching of terrigenous elements by acid precipitation during the Great Acceleration, and calcite precipitation was reduced, producing thin calcite laminae around the GSSP that is marked by a sharp decline in elm pollen (Dutch Elm disease). The lack of bioturbation in well-oxygenated bottom waters, supported by the absence of fossil pigments from obligately anaerobic purple sulfur bacteria, is attributed to elevated salinities and high alkalinity below the chemocline. This aerobic depositional environment, unusual in a meromictic lake, inhibits the mobilization of 239Pu, the proposed primary stratigraphic guide for the Anthropocene

Internet of Things for Sustainable Forestry

Forests and grasslands play an important role in water and air purification, prevention of the soil erosion, and in provision of habitat to wildlife. Internet of Things has a tremendous potential to play a vital role in the forest ecosystem management and stability. The conservation of species and habitats, timber production, prevention of forest soil degradation, forest fire prediction, mitigation, and control can be attained through forest management using Internet of Things. The use and adoption of IoT in forest ecosystem management is challenging due to many factors. Vast geographical areas and limited resources in terms of budget and equipment are some of the limiting factors. In digital forestry, IoT deployment offers effective operations, control, and forecasts for soil erosion, fires, and undesirable depositions. In this chapter, IoT sensing and communication applications are presented for digital forestry systems. Different IoT systems for digital forest monitoring applications are also discussed

Highly symmetric POVMs and their informational power

We discuss the dependence of the Shannon entropy of normalized finite rank-1 POVMs on the choice of the input state, looking for the states that minimize this quantity. To distinguish the class of measurements where the problem can be solved analytically, we introduce the notion of highly symmetric POVMs and classify them in dimension two (for qubits). In this case we prove that the entropy is minimal, and hence the relative entropy (informational power) is maximal, if and only if the input state is orthogonal to one of the states constituting a POVM. The method used in the proof, employing the Michel theory of critical points for group action, the Hermite interpolation and the structure of invariant polynomials for unitary-antiunitary groups, can also be applied in higher dimensions and for other entropy-like functions. The links between entropy minimization and entropic uncertainty relations, the Wehrl entropy and the quantum dynamical entropy are described.Comment: 40 pages, 3 figure

Amenability and covariant injectivity of locally compact quantum groups

As is well known, the equivalence between amenability of a locally compact group G and injectivity of its von Neumann algebra L(G) does not hold in general beyond inner amenable groups. In this paper, we show that the equivalence persists for all locally compact groups if L(G) is considered as a T (L2(G))-module with respect to a natural action. In fact, we prove an appropriate version of this result for every locally compact quantum group

On the operator homology of the Fourier algebra and its cb-multiplier completion

We study various operator homological properties of the Fourier algebra of a locally compact group G. Establishing the converse of two results of Ruan and Xu [35], we show that is relatively operator 1-projective if and only if G is IN, and that is relatively operator 1-flat if and only if G is inner amenable. We also exhibit the first known class of groups for which is not relatively operator C-flat for any . As applications of our techniques, we establish a hereditary property of inner amenability, answer an open question of Lau and Paterson [24], and answer an open question of Anantharaman-Delaroche [1] on the equivalence of inner amenability and Property (W). In the bimodule setting, we show that relative operator 1-biflatness of is equivalent to the existence of a contractive approximate indicator for the diagonal in the Fourier–Stieltjes algebra , thereby establishing the converse to a result of Aristov, Runde, and Spronk [3]. We conjecture that relative 1-biflatness of is equivalent to the existence of a quasi-central bounded approximate identity in , that is, G is QSIN, and verify the conjecture in many special cases. We finish with an application to the operator homology of , giving examples of weakly amenable groups for which is not operator amenable