Single-Qubit Reaped Quantum State Tomography

TL;DR

This paper introduces a scalable quantum state tomography method that uses only three measurements involving a single qubit pointer, simplifying the process for large quantum systems.

Contribution

It proposes a novel tomography scheme requiring only three joint measurements with a single qubit pointer, reducing complexity for large systems.

Findings

Requires only three observables regardless of system size

Uses a single-qubit pointer to 'reap' the wavefunction

Includes an efficient maximum likelihood estimation algorithm

Abstract

Quantum state tomography is the experimental procedure of determining an unknown state. It is not only essential for the verification of resources and processors of quantum information but is also important in its own right with regard to the foundation of quantum mechanics. Standard methods have been elusive for large systems because of the enormous number of observables to be measured and the exponential complexity of data post-processing. Here, we propose a new scheme of quantum state tomography that requires the measurement of only three observables (acting jointly on the system and pointer) regardless of the size of the system. The system is coupled to a "pointer" of single qubit, and the wavefunction of the system is "reaped" onto the pointer upon the measurement of the system. Subsequently, standard two-state tomography on the pointer and classical post-processing are used to reconstruct the quantum state of the system. We also developed an efficient and scalable iterative maximum likelihood algorithm to estimate states from statistically incomplete data.