Quantum entangled fractional Fourier transform based on the IWOP technique

Abstract

In our previous papers, the classical fractional Fourier transform theory was incorporated into the quantum theoretical system using the theoretical method of quantum optics, and the calculation produced quantum mechanical operators corresponding to the generation of fractional Fourier transform. The core function of the coordinate–momentum exchange operators in the addition law of fractional Fourier transform was analyzed too. In this paper, the bivariate operator Hermite polynomial theory and the technique of integration within an ordered product of operators (IWOP) are used to establish the entanglement fractional Fourier transform theory to the extent of quantum. A new function generating formula and an operator for generating quantum entangled fractional Fourier transform are obtained using the fractional Fourier transform relationship in a pair of conjugated entangled state representations.

Wigner function of optical cumulant operator and its dissipation in thermo-entangled state representation

“…where ρ c denotes the density operator of the chaotic light field, [1,2] so it is vital to study the Wigner function [3][4][5] of the optical cumulant operator and its evolution in dissipation. This paper focuses on this topic: first, the Wigner operator [6][7][8] is emphasized as a mixed state representation by using the method of integration within ordered product (IWOP) of operators; [9][10][11][12][13] then, the thermo-entangled state representation [14][15][16][17] is introduced to derive the general evolution formula of the Wigner function; also, the relation to Weyl correspondence [18][19][20] is discussed.…”