Fidelity-optimized quantum state estimation

TL;DR

This paper introduces an optimized Bayesian method for quantum state estimation that adaptively chooses measurements to maximize fidelity, demonstrating improved accuracy for single and two-qubit states.

Contribution

It presents a self-correcting, fidelity-optimized Bayesian protocol for quantum state estimation, including practical variants with limited measurement bases.

Findings

Enhanced fidelity in state estimation for single-qubit and two-qubit systems.

Outperforms existing methods in accuracy and efficiency.

Effective even with restricted measurement bases.

Abstract

We describe an optimized, self-correcting procedure for the Bayesian inference of pure quantum states. By analyzing the history of measurement outcomes at each step, the procedure returns the most likely pure state, as well as the optimal basis for the measurement that is to follow. The latter is chosen to maximize, on average, the fidelity of the most likely state after the measurement. We also consider a practical variant of this protocol, where the available measurement bases are restricted to certain limited sets of bases. We demonstrate the success of our method by considering in detail the single-qubit and two-qubit cases, and comparing the performance of our method against other existing methods.