Comparing weak and projective measurements for quantum state tomography of a single-qubit system

TL;DR

This paper investigates the effectiveness of weak measurements in quantum state tomography of a single qubit, comparing their performance to traditional projective measurements through simulations.

Contribution

It applies and tests the Das-Arvind weak measurement tomography protocol across different measurement strengths and ensemble sizes, providing a detailed comparison with projective methods.

Findings

Weak measurements can extract quantum state information with less disturbance.

The performance of weak measurements varies with measurement strength and ensemble size.

Results align with current understanding of measurement impacts on quantum state estimation.

Abstract

We explore the use of weak quantum measurements for single-qubit quantum state tomography processes. Weak measurements are those where the coupling between the qubit and the measurement apparatus is weak; this results in the quantum state being disturbed less than in the case of a projective measurement. We employ a weak measurement tomography protocol developed by Das and Arvind, which they claim offers a new method of extracting information from quantum systems. We test the Das-Arvind scheme for various measurement strengths, and ensemble sizes, and reproduce their results using a sequential stochastic simulation. Lastly, we place these results in the context of current understanding of weak and projective measurements.