A novel 3D entangled wavelet transformation and its properties

Abstract

Based on the quantum mechanics representation, we propose a novel 3D entangled wavelet transformation. This kind of three entangled state representation can be generated theoretically by using a two-cascaded beam splitter, which has the completeness and orthogonal property. Some properties of 3D WTs are discussed, including the Parseval theory of 3D WTs, its inverse formula, and the orthogonality of the mother wavelets in parameter space. In addition, the mother wavelet condition for the 3D WTs is also derived.