Achieving quantum precision limit in adaptive qubit state tomography

TL;DR

This paper reports the first experimental achievement of the quantum precision limit in adaptive qubit state tomography, demonstrating a simple yet powerful two-step adaptive strategy that optimizes measurement accuracy for optical polarization qubits.

Contribution

It introduces a practical two-step adaptive method that attains the quantum precision limit in qubit tomography, advancing experimental capabilities and theoretical understanding.

Findings

Achieved quantum precision limit in adaptive qubit tomography

Implemented a simple two-step adaptive measurement strategy

Enhanced understanding of quantum estimation and measurement tradeoffs

Abstract

The precision limit in quantum state tomography is of great interest not only to practical applications but also to foundational studies. However, little is known about this subject in the multiparameter setting even theoretically due to the subtle information tradeoff among incompatible observables. In the case of a qubit, the theoretic precision limit was determined by Hayashi as well as Gill and Massar, but attaining the precision limit in experiments has remained a challenging task. Here we report the first experiment which achieves this precision limit in adaptive quantum state tomography on optical polarization qubits. The two-step adaptive strategy employed in our experiment is very easy to implement in practice. Yet it is surprisingly powerful in optimizing most figures of merit of practical interest. Our study may have significant implications for multiparameter quantum estimation problems, such as quantum metrology. Meanwhile, it may promote our understanding about the complementarity principle and uncertainty relations from the information theoretic perspective.