Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Frontiers in Optics

Implementation of Quantum and Classical Discrete Fractional Fourier Transforms

Armando Pérez-Leija, Steffen Weimann, Maxime Lebugle, Markus Gräfe, René Heilmann, Stefan Nolte, H. M. Moya-Cessa, Demetrios N. Christodoulides, Alexander Szameit

Published Jan 1, 2015• 3 citations
Publisher

Abstract

We report on the experimental realization of quantum and classical discrete fractional Fourier transforms (DFrFT) using photonic lattices. Our approach is fully integrated and free of bulk optical components.
DOI
10.1364/fio.2015.fth2d.4

Related papers

Implementation of quantum discrete fractional Fourier transform

Markus Gräfe, Steffen Weimann, Armando Pérez-Leija +7 more

In this work we experimentally demonstrate the realization of the discrete fractional Fourier transforms (DFrFT) in both the classical and quantum realm. Our approach is fully integrated and free of bulk optical components.

Quantum Information and Measurement (QIM)•Jan 1, 2017•0 citations

Implementation of the Classical and Quantum Fourier Transform in Photonic Lattices

Steffen Weimann, Armando Pérez-Leija, Maxime Lebugle +1 more

We report on the experimental realization of an optical version of the fractional and standard Fourier transform using discrete photonic lattices. Our approach is fully integrated and free of bulk optical components. We investigate the transformation of classical and quantum light.

•Jan 1, 2015•0 citations

Implementation of quantum and classical discrete fractional Fourier transforms

Steffen Weimann, Armando Pérez-Leija, Maxime Lebugle +9 more

Fourier transforms, integer and fractional, are ubiquitous mathematical tools in basic and applied science. Certainly, since the ordinary Fourier transform is merely a particular case of a continuous set of fractional Fourier domains, every property and application of the ordinary Fourier transform becomes a special case of the fractional Fourier transform. Despite the great practical importance of the discrete Fourier transform, implementation of fractional orders of the corresponding discrete operation has been elusive. Here we report classical and quantum optical realizations of the discrete fractional Fourier transform. In the context of classical optics, we implement discrete fractional Fourier transforms of exemplary wave functions and experimentally demonstrate the shift theorem. Moreover, we apply this approach in the quantum realm to Fourier transform separable and path-entangled biphoton wave functions. The proposed approach is versatile and could find applications in various fields where Fourier transforms are essential tools.

arXiv:1508.00033•Nature Communications•Mar 23, 2016•120 citations

On the Scaled Fractional Fourier Transformation Operator

Fan Hong‐Yi, Liyun Hu

Based on our previous study [Chin. Phys. Lett. 24 (2007) 2238] in which the Fresnel operator corresponding to classical Fresnel transform was introduced, we derive the fractional Fourier transformation operator, and the optical operator method is then enriched.

Chinese Physics Letters•Feb 1, 2008•10 citations

A Cross-Layer Secure Communication Model Based on Discrete Fractional Fourier Fransform (DFRFT)

Hong Wen, Jie Tang, Jinsong Wu +6 more

Discrete fractional Fourier transform (DFRFT) is a generalization of discrete Fourier transform. There are a number of DFRFT proposals, which are useful for various signal processing applications. This paper investigates practical solutions toward the construction of unconditionally secure communication systems based on DFRFT via cross-layer approach. By introducing a distort signal parameter, the sender randomly flip-flops between the distort signal parameter and the general signal parameter to confuse the attacker. The advantages of the legitimate partners are guaranteed. We extend the advantages between legitimate partners via developing novel security codes on top of the proposed cross-layer DFRFT security communication model, aiming to achieve an error-free legitimate channel while preventing the eavesdropper from any useful information. Thus, a cross-layer strong mobile communication secure model is built.

IEEE Transactions on Emerging Topics in Computing•Nov 6, 2014•44 citations

Implementing quantum Fourier transform with integrated photonic devices

Gelo Noel M. Tabia

Bulletin of the American Physical Society•Mar 6, 2014•0 citations
Fourier transforms, integer and fractional, are ubiquitous mathematical tools in basic and applied science. Certainly, since the ordinary Fourier transform is merely a particular case of a continuous set of fractional Fourier domains, every property and application of the ordinary Fourier transform becomes a special case of the fractional Fourier transform. Despite the great practical importance of the discrete Fourier transform, implementation of fractional orders of the corresponding discrete operation has been elusive. Here we report classical and quantum optical realizations of the discrete fractional Fourier transform. In the context of classical optics, we implement discrete fractional Fourier transforms of exemplary wave functions and experimentally demonstrate the shift theorem. Moreover, we apply this approach in the quantum realm to Fourier transform separable and path-entangled biphoton wave functions. The proposed approach is versatile and could find applications in various fields where Fourier transforms are essential tools.
Discrete fractional Fourier transform (DFRFT) is a generalization of discrete Fourier transform. There are a number of DFRFT proposals, which are useful for various signal processing applications. This paper investigates practical solutions toward the construction of unconditionally secure communication systems based on DFRFT via cross-layer approach. By introducing a distort signal parameter, the sender randomly flip-flops between the distort signal parameter and the general signal parameter to confuse the attacker. The advantages of the legitimate partners are guaranteed. We extend the advantages between legitimate partners via developing novel security codes on top of the proposed cross-layer DFRFT security communication model, aiming to achieve an error-free legitimate channel while preventing the eavesdropper from any useful information. Thus, a cross-layer strong mobile communication secure model is built.