Quantum tomography with wavelet transform in Banach space on Homogeneous space

TL;DR

This paper explores the use of wavelet transforms in Banach spaces on homogeneous spaces to unify and analyze various quantum tomography methods, revealing their atomic decomposition and frame structures.

Contribution

It introduces a wavelet-based Banach space framework that connects multiple quantum tomography techniques and discusses their atomic and frame properties.

Findings

Unified wavelet formalism for quantum tomography

Atomic decomposition and Banach frame analysis of tomographic methods

Connection between wavelet formalism and Q-function in quantum states

Abstract

The intimate connection between the Banach space wavelet reconstruction method on homogeneous spaces with both singular and nonsingular vacuum vectors, and some of well known quantum tomographies, such as: Moyal-representation for a spin, discrete phase space tomography, tomography of a free particle, Homodyne tomography, phase space tomography and SU(1,1) tomography is explained. Also both the atomic decomposition and banach frame nature of these quantum tomographic examples is explained in details. Finally the connection between the wavelet formalism on Banach space and Q-function is discussed.