Beating three-parameter precision trade-offs with entangling collective measurements

TL;DR

This paper demonstrates experimentally that entangling collective measurements on two qubits can surpass the fundamental precision limits of individual measurements in estimating three parameters of a qubit, deepening understanding of quantum uncertainty.

Contribution

The study provides the first experimental verification that optimal collective measurements can beat the quantum trade-offs in three-parameter qubit estimation.

Findings

Experimental violation of the entanglement-free trade-off relation by 16 standard deviations.

Achieved tomography precision beyond any individual measurement scheme.

Confirmed that collective measurements can surpass fundamental quantum limits in a three-parameter setting.

Abstract

Quantum-mechanical incompatibility, which precludes the simultaneous precise measurement of non-commuting observables, imposes fundamental limits on the rate at which classical information can be extracted. While the potential to surpass these limits using entangling collective measurements has been explored for two parameters, the regime of three or more parameters remains largely unexplored despite its fundamental and technological importance. Here, we investigate the three-parameter trade-off relations for estimating the Bloch vector components of a qubit, comparing conventional individual measurements with entangling collective measurements. We theoretically derive and experimentally implement optimal collective measurements on two identically prepared qubits using a programmable photonic circuit. Our experimental results demonstrate a clear violation of the entanglement-free trade-off relation -- by an average of 16 standard deviations -- achieving a tomography precision beyond the reach of any individual measurement scheme. This work directly confirms that optimal collective measurements can surpass the fundamental quantum limits of individual schemes in a three-parameter setting -- thereby deepening our understanding of quantum uncertainty relations beyond the two-parameter regime and providing a clear strategy to overcome the precision trade-offs imposed by quantum incompatibility.