Quantum state tomography from sequential measurement of two variables in a single setup

TL;DR

This paper presents an efficient method for quantum state tomography using sequential measurements of two observables related by a discrete Fourier transform, applicable to various states and experimental setups.

Contribution

It introduces a novel tomography scheme based on sequential measurements of Fourier-related observables, applicable to arbitrary states and fixed experimental setups.

Findings

Efficient quantum state determination with sequential measurements.

Applicable to pure and mixed states in finite-dimensional spaces.

Introduces Moyal quasicharacteristic function for finite dimensions.

Abstract

We demonstrate that the task of determining an unknown quantum state can be accomplished efficiently by making a sequential measurement of two observables $\hat{A}$ and $\hat{B}$, provided that the two observables are chosen in such a way that their eigenstates may form bases connected by a discrete Fourier transform. The state can be pure or mixed, the dimension of the Hilbert space and the coupling strength are arbitrary, and the experimental setup is fixed. The concept of Moyal quasicharacteristic function is introduced for finite-dimensional Hilbert spaces.