Limitations for adaptive quantum state tomography in the presence of detector noise

TL;DR

This paper investigates how readout noise affects the advantages of adaptive quantum state tomography, showing that noise eliminates quadratic scaling benefits but adaptive methods still offer practical improvements with proper calibration.

Contribution

It provides analytical and numerical evidence that readout noise removes asymptotic advantages of adaptive strategies, highlighting the importance of detector calibration for practical benefits.

Findings

Readout noise eliminates quadratic scaling advantage of adaptive tomography.

Finite measurement statistics show a transition from ideal to sub-optimal scaling.

Proper detector calibration enhances the practical benefits of adaptive strategies.

Abstract

Assumption-free reconstruction of quantum states from measurements is essential for benchmarking and certifying quantum devices, but it remains difficult due to the extensive measurement statistics and experimental resources it demands. An approach to alleviating these demands is provided by adaptive measurement strategies, which can yield up to a quadratic improvement in reconstruction accuracy for pure states by dynamically optimizing measurement settings during data acquisition. A key open question is whether these asymptotic advantages remain in realistic experiments, where readout is inevitably noisy. In this work, we analyze the impact of readout noise on adaptive quantum state tomography with readout-error mitigation, focusing on the challenging regime of reconstructing pure states using mixed-state estimators. Using analytical arguments based on Fisher information optimization and extensive numerical simulations using Bayesian inference, we show that any nonzero readout noise eliminates the asymptotic quadratic scaling advantage of adaptive strategies. We numerically investigate the behavior for finite measurement statistics for single- and two-qubit systems with exact readout-error mitigation and find a gradual transition from ideal to sub-optimal scaling. We furthermore investigate realistic scenarios where detector tomography is performed with a limited number of state copies for calibration, showing that insufficient detector characterization leads to estimator bias and limited reconstruction accuracy. Although our result imposes an upper bound on the reconstruction accuracy that can be achieved with adaptive strategies, we nevertheless observe numerically a constant-factor gain in reconstruction accuracy, which becomes larger as the readout noise decreases. This indicates potential practical benefits in using adaptive measurement strategies in well-calibrated experiments.