Near-optimal quantum tomography: estimators and bounds

Abstract

We give bounds on the average fidelity achievable by any quantum state estimator, which is arguably the most prominently used figure of merit in quantum state tomography. Moreover, these bounds can be computed online---that is, while the experiment is running. We show numerically that these bounds are quite tight for relevant distributions of density matrices. We also show that the Bayesian mean estimator is ideal in the sense of performing close to the bound without requiring optimization. Our results hold for all finite dimensional quantum systems.

These guys submitted v1 with a clickbait title. You probably could have guessed what happened next

References in corpus (6)

• Direct Fidelity Estimation from Few Pauli Measurements
• Symmetrised Characterisation of Noisy Quantum Processes
• Robust Online Hamiltonian Learning
• Single shot parameter estimation via continuous quantum measurement
• Single Shot Quantum State Estimation via a Continuous Measurement in the Strong Backaction Regime
• Accurate quantum state estimation via "Keeping the experimentalist honest"

Cited by in corpus (11)

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• Operational, gauge-free quantum tomography
• Maximum likelihood quantum state tomography is inadmissible
• Minimax quantum state estimation under Bregman divergence
• An efficient adaptive MCMC algorithm for Pseudo-Bayesian quantum tomography
• Resource-Efficient Cross-Platform Verification with Modular Superconducting Devices
• Bayes estimator for multinomial parameters and Bhattacharyya distances
• Coarse-graining in retrodictive quantum state tomography
• Principles of quantum functional testing