Scalable multimode entanglement based on efficient squeezing of propagation eigenmodes

Continuous-variable encoding of quantum information in the optical domain has recently yielded large temporal and spectral entangled states instrumental for quantum computing and quantum communication. We introduce a protocol for the generation of spatial multipartite entanglement based on phase-matching of a propagation eigenmode in a monolithic photonic device: the array of quadratic nonlinear waveguides. We theoretically demonstrate in the spontaneous parametric downconversion regime the generation of large multipartite entangled states useful for multimode quantum networks. Our protocol is remarkably simple and robust as it does not rely on specific values of coupling, nonlinearity or length of the sample.Comment: 8 pages, 5 figures, title modified and new results added. Accepted for publication in Physical Review Researc

Gradual sub-lattice reduction and a new complexity for factoring polynomials

We present a lattice algorithm specifically designed for some classical applications of lattice reduction. The applications are for lattice bases with a generalized knapsack-type structure, where the target vectors are boundably short. For such applications, the complexity of the algorithm improves traditional lattice reduction by replacing some dependence on the bit-length of the input vectors by some dependence on the bound for the output vectors. If the bit-length of the target vectors is unrelated to the bit-length of the input, then our algorithm is only linear in the bit-length of the input entries, which is an improvement over the quadratic complexity floating-point LLL algorithms. To illustrate the usefulness of this algorithm we show that a direct application to factoring univariate polynomials over the integers leads to the first complexity bound improvement since 1984. A second application is algebraic number reconstruction, where a new complexity bound is obtained as well

Correlated twin-photon generation in a silicon nitride loaded thin film PPLN waveguide

Photon-pair sources based on thin film lithium niobate on insulator technology have a great potential for integrated optical quantum information processing. We report on such a source of correlated twin-photon pairs generated by spontaneous parametric down conversion in a silicon nitride (SiN) rib loaded thin film periodically poled lithium niobate (LN) waveguide. The generated correlated photon pairs have a wavelength centred at 1560 nm compatible with present telecom infrastructure, a large bandwidth (21 THz) and a brightness of ∼2.5 × 105 pairs/s/mW/GHz. Using the Hanbury Brown and Twiss effect, we have also shown heralded single photon emission, achieving an autocorrelation g (2) H (0) ≃ 0.04.Antoine Henry, David Barral, Isabelle Zaquine, Andreas Boes, Arnan Mitchell, Nadia Belabas, and Kamel Bencheik

Number Fields Ramified at One Prime

Abstract. For G a finite group and p a prime, a G-p field is a Galois number field K with Gal(K/Q) ∼ = G and disc(K) = ±pa for some a. We study the existence of G-p fields for fixed G and varying p. For G a finite group and p a prime, we define a G-p field to be a Galois number field K ⊂ C satisfying Gal(K/Q) ∼ = G and disc(K) = ±pa for some a. Let KG,p denote the finite, and often empty, set of G-p fields. The sets KG,p have been studied mainly from the point of view of fixing p and varying G; see [Har94], for example. We take the opposite point of view, as we fix G and let p vary. Given a finite group G, we let PG be the sequence of primes where each prime p is listed |KG,p | times. We determine, for various groups G, the first few primes in PG and their corresponding fields. Only the primes p dividing |G | can be wildly ramified in a G-p field, and so the sequences PG which are infinite are dominated by tamely ramified fields. In Sections 1, 2, and 3, we consider the cases when G is solvable with length 1, 2, and ≥ 3 respectively, using mainly class field theory. Section 4 deals wit

Discriminants cubiques et progressions arithmétiques

Algorithmique des fonctions