5,385 research outputs found
Multi-dimensional metric approximation by primitive points
We refine metrical statements in the style of the Khintchine-Groshev Theorem
by requiring certain coprimality constraints on the coordinates of the integer
solutions
Quantum key distribution session with 16-dimensional photonic states
The secure transfer of information is an important problem in modern
telecommunications. Quantum key distribution (QKD) provides a solution to this
problem by using individual quantum systems to generate correlated bits between
remote parties, that can be used to extract a secret key. QKD with
D-dimensional quantum channels provides security advantages that grow with
increasing D. However, the vast majority of QKD implementations has been
restricted to two dimensions. Here we demonstrate the feasibility of using
higher dimensions for real-world quantum cryptography by performing, for the
first time, a fully automated QKD session based on the BB84 protocol with
16-dimensional quantum states. Information is encoded in the single-photon
transverse momentum and the required states are dynamically generated with
programmable spatial light modulators. Our setup paves the way for future
developments in the field of experimental high-dimensional QKD.Comment: 8 pages, 3 figure
On invariant measures of the Euclidean algorithm
We study the ergodic properties of the additive Euclidean algorithm defined in . A natural extension of is obtained using the action of on a subset of . We prove that, while is an ergodic transformation with an infinite invariant measure equivalent to the Lebesgue measure, the invariant measure is not unique up to scalar multiples, and in fact there is a continuous family of such measures
Sendrá el tenor de sólidos solubles totales de los frutos de cucumis melo influenciado por carlavirus?
Melão; Cucumis melo; Insetos; Mosca-Branca; Bemisia tabaci; Teor de sólido
Lift-up, Kelvin-Helmholtz and Orr mechanisms in turbulent jets
Three amplification mechanisms present in turbulent jets, namely lift-up, Kelvin–Helmholtz and Orr, are characterized via global resolvent analysis and spectral proper orthogonal decomposition (SPOD) over a range of Mach numbers. The lift-up mechanism was recently identified in turbulent jets via local analysis by Nogueira et al. (J. Fluid Mech., vol. 873, 2019, pp. 211–237) at low Strouhal number ( St ) and non-zero azimuthal wavenumbers ( m ). In these limits, a global SPOD analysis of data from high-fidelity simulations reveals streamwise vortices and streaks similar to those found in turbulent wall-bounded flows. These structures are in qualitative agreement with the global resolvent analysis, which shows that they are a response to upstream forcing of streamwise vorticity near the nozzle exit. Analysis of mode shapes, component-wise amplitudes and sensitivity analysis distinguishes the three mechanisms and the regions of frequency–wavenumber space where each dominates, finding lift-up to be dominant as St/m→0 . Finally, SPOD and resolvent analyses of localized regions show that the lift-up mechanism is present throughout the jet, with a dominant azimuthal wavenumber inversely proportional to streamwise distance from the nozzle, with streaks of azimuthal wavenumber exceeding five near the nozzle, and wavenumbers one and two most energetic far downstream of the potential core
Multimode Hong-Ou-Mandel Interferometry
We review some recent experiments based upon multimode two-photon
interference of photon pairs created by spontaneous parametric down-conversion.
The new element provided by these experiments is the inclusion of the
transverse spatial profiles of the pump, signal and idler fields. We discuss
multimode Hong-Ou-Mandel interference, and show that the transverse profile of
the pump beam can be manipulated in order to control two-photon interference.
We present the basic theory and experimental results as well as several
applications to the field of quantum information.Comment: 20 pages, 14 figures, Brief Review to be published in Modern Physics
Letters
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