Precision-guaranteed quantum tomography
Takanori Sugiyama, Peter S. Turner, Mio Murao

TL;DR
This paper introduces a rigorous estimator for quantum state tomography that guarantees the precision of state preparation, providing explicit probability bounds applicable to various measurement schemes and loss functions.
Contribution
It presents a new estimator with proven high-probability closeness to the true state, enabling rigorous evaluation of quantum state preparation accuracy.
Findings
Derived explicit probability bounds for estimator accuracy
Applicable to any informationally complete measurement set
Works for multiple data sets and various loss functions
Abstract
Quantum state tomography is the standard tool in current experiments for verifying that a state prepared in the lab is close to an ideal target state, but up to now there were no rigorous methods for evaluating the precision of the state preparation in tomographic experiments. We propose a new estimator for quantum state tomography, and prove that the (always physical) estimates will be close to the true prepared state with high probability. We derive an explicit formula for evaluating how high the probability is for an arbitrary finite-dimensional system and explicitly give the one- and two-qubit cases as examples. This formula applies for any informationally complete sets of measurements, arbitrary finite number of data sets, and general loss functions including the infidelity, the Hilbert-Schmidt, and the trace distances. Using the formula, we can evaluate not only the difference…
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