We report on the generation of continuous-variable hyperentanglement of polarization and orbital angular momentum with a type II optical parametric oscillator. By compensating for the astigmatism between spatial modes, we produce an entangled pair of Hermite-Gauss beams. From correlations measurements, we verify the existence of continuous-variable hyperentanglement by the general entanglement ...

This paper presents new properties of Primitive Pythagorean Triples (PPT) that have relevance in applications where events of different probability need to be generated and in cryptography.

The looping constant ξ(Z) is the expected number of neighbors of the origin that lie on the infinite loop-erased random walk in Z. Poghosyan, Priezzhev and Ruelle, and independently, Kenyon and Wilson, proved recently that ξ(Z) = 54 . We consider the infinite volume limits as G ↑ Z of three different statistics: (1) The expected length of the cycle in a uniform spanning unicycle of G; (2) The e...

« paree que j'ai maintenant des petits enfants, j 'ai souveru envie de raconter des histoires. c 'est la fonction naturelle des grands-peres, et peut-etre leur grand merite. » nous venons de citer un extrait de « la gloire de mon pere » un des ouvrages de pagnol. c'est un ecrivain conternporain francais qui a commence sa carriere au theatre. on peut dire qu'il a fait qu...

Abstract Strawberry ( Fragaria × ananassa Duch.) is one of the most significant horticultural cash crops in world. The study aimed to identify and analyse 2,930 articles review type papers strawberry research from Plant Sciences category based on Web Science. Papers mainly written English (2,894, 98.771%), were a total 8,838 authors, 96 countries/territories, 1,845 organisations published 197 j...

We study asymptotic properties of the Green metric associated with transient random walks on countable groups. We prove that the rate of escape of the random walk computed in the Green metric equals its asymptotic entropy. The proof relies on integral representations of both quantities with the extended Martin kernel. In the case of finitely generated groups, where this result is known (Benjami...

We construct a class of multipartite states possessing rotational SO(3) symmetry – these are states of K spin-jA particles and K spin-jB particles. The construction of symmetric states follows our two recent papers devoted to unitary and orthogonal multipartite symmetry. We study basic properties of multipartite SO(3) symmetric states: separability criteria and multi-PPT conditions.

E. Nichols ([email protected]) and S. Spector, Center for Biodiversity and Conservation, Invertebrate Conservation Program, American Museum of Natural History, Central Park West at 79th St., New York, NY 100245193, USA. T. A. Gardner, Biology Dept, Univ. Federal de Lavras, Lavras MG, 37200-000, Brazil, and Dept of Zoology, Univ. of Cambridge, Downing Street, Cambridge, CB2 3EJ, UK. C. A. Peres, ...

For a finite undirected graph G = (V, E), let pu,v(t) denote the probability that a continuoustime random walk starting at vertex u is in v at time t. In this note we give an example of a Cayley graph G and two vertices u, v ∈ G for which the function ru,v(t) = pu,v(t) pu,u(t) t ≥ 0 is not monotonically non-decreasing. This answers a question asked by Peres in 2013.

We show that an experimental demonstration of quantum contextuality using 2 degrees of freedom of single neutrons based on a violation of an inequality derived from the Peres-Mermin proof of the Kochen-Specker theorem would be more conclusive than those obtained from previous experiments involving pairs of ions [M. A. Rowe, Nature (London) 409, 791 (2001)10.1038/35057215] and single neutrons [Y...