Fractional squeezing-Hankel transform based on the induced entangled state representations

Abstract

Based on the fact that the quantum mechanical version of Hankel transform kernel (the Bessel function) is just the transform between |q, r⟩ and (s, r ′ |, two induced entangled state representations are given, and working with them we derive fractional squeezing-Hankel transform (FrSHT) caused by the operator e −iα(a † 1 a † 2 +a 1 a 2 ) e −iπa † 2 a 2 , which is an entangled fractional squeezing transform operator. The additive rule of the FrSHT can be explicitly proved.

Optical wavelet-fractional squeezing combinatorial transform

“…In the following we shall tackle this problem quantum-mechanically, i.e., the way we successfully combine them to realize the integration transform kernel of WFrST is making full use of the completeness relation of Dirac's ket-bra representation. [17] We start with recasting the WT and the FrST into the context of quantum-mechanics in Sections 2 and 3. In Section 4, by combining the WT and the FrST quantum mechanically, we propose the optical wavelet-fractional squeezing combinatorial transform and derive its corresponding operator by using the method of integration within ordered product (IWOP) of operators.…”