Adaptive tomography of qubits: Purity versus statistical fluctuations

TL;DR

This paper presents an adaptive qubit tomography method that achieves optimal accuracy scaling with the number of measurements, especially effective for nearly-pure states, and explores the impact of state purity on measurement fluctuations.

Contribution

It introduces an adaptive tomography protocol with $O(1/N)$ accuracy scaling and analyzes how state purity influences measurement fluctuations and characterization performance.

Findings

Achieves $O(1/N)$ accuracy scaling for large N

Highlights differences in characterizing nearly-pure versus pure or mixed states

Provides insights into the role of statistical fluctuations in state estimation

Abstract

The success of quantum information processing applications relies on accurate and efficient characterization of quantum states, especially nearly-pure states. In this work, we investigate a procedure for adaptive qubit state tomography which achieves $O(1/N)$ scaling in accuracy for large $N$. We analyze the performance of the adaptive protocol on the characterization of pure, mixed and nearly-pure states, and clarify the interplay between the purity of the state and the statistical fluctuations of the measurement results. Our results highlight the subtle difference between the characterization of nearly-pure states and those of pure or highly mixed states.