Recursively Adaptive Quantum State Tomography: Theory and Two-qubit Experiment

TL;DR

This paper introduces a recursively adaptive quantum state tomography protocol that enhances accuracy in two-qubit systems through adaptive measurements and recursive estimation, outperforming traditional methods and achieving significant error reduction.

Contribution

The paper presents a novel RAQST protocol with recursive linear regression and adaptive measurement strategies, demonstrating superior performance over existing methods in two-qubit quantum state tomography.

Findings

RAQST outperforms MUB-based protocols in simulations.

Experimental implementation reduces systematic errors by 100-fold.

RAQST is especially effective for reconstructing maximally entangled states.

Abstract

Adaptive techniques have important potential for wide applications in enhancing precision of quantum parameter estimation. We present a recursively adaptive quantum state tomography (RAQST) protocol for finite dimensional quantum systems and experimentally implement the adaptive tomography protocol on two-qubit systems. In this RAQST protocol, an adaptive measurement strategy and a recursive linear regression estimation algorithm are performed. Numerical results show that our RAQST protocol can outperform the tomography protocols using mutually unbiased bases (MUB) and the two-stage MUB adaptive strategy even with the simplest product measurements. When nonlocal measurements are available, our RAQST can beat the Gill-Massar bound for a wide range of quantum states with a modest number of copies. We use only the simplest product measurements to implement two-qubit tomography experiments. In the experiments, we use error-compensation techniques to tackle systematic error due to misalignments and imperfection of wave plates, and achieve about 100-fold reduction of the systematic error. The experimental results demonstrate that the improvement of RAQST over nonadaptive tomography is significant for states with a high level of purity. Our results also show that this recursively adaptive tomography method is particularly effective for the reconstruction of maximally entangled states, which are important resources in quantum information.