aqora

Implementation of Quantum and Classical Discrete Fractional Fourier Transforms

Armando Pérez-Leija, Steffen Weimann, Maxime Lebugle +6 more

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.

Frontiers in OpticsJan 1, 20153 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, 20150 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.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:1508.00033Nature CommunicationsMar 23, 2016120 citations

Experimental realization of discrete fourier transformation on NMR quantum computers

Li‐Yun Fu, J. Luo, Xiao Li +1 more

Applied Magnetic ResonanceJun 1, 200012 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.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 ComputingNov 6, 201444 citations

Quantum Theory of Optical Fractional Fourier Transform

张科 Ke ZHANG, 李兰兰 Lan-lan LI, 余海军 Hai-jun YU +2 more

ACTA PHOTONICA SINICAJan 1, 20202 citations

Implementation of quantum discrete fractional Fourier transform

Abstract

Related papers

Implementation of quantum discrete fractional Fourier transform

Abstract

Related papers