Adaption of Collins formula to fractional Fourier transform studied in the entangled state representation of quantum optics

Abstract

Adaption of Collins diffraction formula to the fractional Fourier transform in complex form (FFT-C) is demonstrated in entangled state |η⟩ representation of quantum optics. The additivity property of FFT-C corresponding to Collins formula has been proved by using group multiplication of the Fresnel operator and the quantum mechanical version of the Collins formula.

Keywords:

• Collins diffraction formula
• fractional Fourier transform
• entangled state representation
• Fresnel operator

Acknowledgements

We sincerely thank the referee for his useful suggestion. This work was supported by the National Natural Science Foundation of China (Grant Nos. 10775097 and 10475056).