Saturating the Quantum Cram\'er--Rao Bound in Prioritised Parameter Estimation

TL;DR

This paper demonstrates that in quantum multi-parameter estimation, it is possible to optimize information gain for one parameter without entirely losing information about others, revealing new trade-off structures.

Contribution

The authors show that certain quantum systems allow simultaneous near-optimal estimation of multiple parameters, challenging traditional trade-off limitations.

Findings

Achieved maximal information for one parameter without fully losing others

Derived new trade-off relations in quantum parameter estimation

Implemented optimal entangling measurement on a trapped-ion quantum computer

Abstract

Measurement incompatibility is a cornerstone of quantum mechanics. In the context of estimating multiple parameters of a quantum system, this manifests as a fundamental trade-off between the precisions with which different parameters can be estimated. Often, a parameter can be optimally measured, but at the cost of gaining no information about incompatible parameters. Here, we report that there are systems where one parameter's information can be maximised while not completely losing information about the other parameters. In doing so, we find attainable trade-off relations for quantum parameter estimation with a structure that is different to typical Heisenberg-type trade-offs. We demonstrate our findings by implementing an optimal entangling measurement on a Quantinuum trapped-ion quantum computer.