Continuous phase-space representations for finite-dimensional quantum states and their tomography

TL;DR

This paper develops a unified framework for continuous phase-space representations of finite-dimensional quantum states, clarifying their interrelations and applications in quantum state tomography, with connections to the infinite-dimensional case.

Contribution

It introduces a comprehensive approach that unifies various phase-space representations for finite-dimensional quantum states and elucidates their relation to the infinite-dimensional limit.

Findings

Unified phase-space framework for finite-dimensional states

Clarified relations among different phase-space representations

Connected finite-dimensional and infinite-dimensional cases

Abstract

Continuous phase spaces have become a powerful tool for describing, analyzing, and tomographically reconstructing quantum states in quantum optics and beyond. A plethora of these phase-space techniques are known, however a thorough understanding of their relations was still lacking for finite-dimensional quantum states. We present a unified approach to continuous phase-space representations which highlights their relations and tomography. The infinite-dimensional case from quantum optics is then recovered in the large-spin limit.