Quantum state tomography using a single apparatus

TL;DR

This paper proposes a method for quantum state tomography of a two-level system using a single apparatus by measuring two commuting observables through atom-field interaction, simplifying the process of state determination.

Contribution

It introduces a novel approach to quantum state tomography that employs a single measurement setup with commuting variables, reducing complexity compared to traditional methods.

Findings

Successful extraction of the density matrix from commuting measurements

Advantages include simplified experimental setup and potential for broader applications

Demonstrates feasibility within the Jaynes--Cummings model framework

Abstract

The density matrix of a two-level system (spin, atom) is usually determined by measuring the three non-commuting components of the Pauli vector. This density matrix can also be obtained via the measurement data of two commuting variables, using a single apparatus. This is done by coupling the two-level system to a mode of radiation field, where the atom-field interaction is described with the Jaynes--Cummings model. The mode starts its evolution from a known coherent state. The unknown initial state of the atom is found by measuring two commuting observables: the population difference of the atom and the photon number of the field. We discuss the advantages of this setup and its possible applications.