https://doi.org/10.1140/epjd/e2002-00192-1
EPR entangled states and complex fractional Fourier transformation*
1
CCAST (World Laboratory), P.O. Box 8730, 100080 Beijing, P.R. China
2
Department of Material Science and Engineering, University of Science and Technology of China, Hefei, Anhui 230026, P.R. China
Corresponding author: a fhym@ustc.edu.cn
Received:
21
February
2002
Revised:
1
June
2002
Published online:
24
September
2002
Starting from the Einstein-Podolsky-Rosen entangled state representations of continuous variables we derive a new formulation of complex fractional Fourier transformation (CFFT). We find that two-variable Hermite polynomials are just the eigenmodes of the CFFT. In this way the CFFT is linked to the appropriate operator transformation between two kinds of entangled states in the context of quantum mechanics. In so doing, the CFFT of quantum mechanical wave functions can be derived more directly and concisely.
PACS: 03.65.Ud – Entanglement and quantum nonlocality (e.g. EPR paradox, Bell's inequalities, GHZ states, etc.) / 42.30.Lr – Modulation and optical transfer functions / 42.50.Dv – Nonclassical field states; squeezed, antibunched, and sub-Poissonian states; operational definitions of the phase of the field; phase measurements
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2002
