J. van de Graaf

collaborators

2 papers

math.NT2021

A fast recurrence for Fibonacci and Lucas numbers

Jeroen van de Graaf

We derive the double recurrence $e_{n} = \frac{1}{2} (a_{n - 1} + 5 b_{n - 1}); f_{n} = \frac{1}{2} (a_{n - 1} + b_{n - 1})$ with $e_{0} = 2; f_{0} = 0$ for the Fibonacci numbers, leading to an extremely si…

quant-ph2016

Quantum key distribution by phase flipping of coherent states of light

G. A. Barbosa, J. van de Graaf, P. Mateus +1

In this paper we present quantum key distribution protocol that, instead of single qubits, uses mesoscopic coherent states of light $∣ α ⟩$ to encode bit values of a randomly g…