The precision with which multiple parameters of a quantum system can be estimated is restricted by the uncertainty principle: the optimal measurements for estimating each parameter are generally incompatible and thus cannot be implemented simultaneously. The ANU quantum optics group has been investigating the fundamental limits to quantum multiparameter estimation and how quantum entanglement can enhance measurement precision.

A central task in multiparameter estimation is determining the possible mean squared errors of estimators for the parameters. In 2021, Lorcán Conlon developed an efficient way to calculate a lower bound that applies to estimating any number of parameters using measurements performed on individual copies of the probe state, called the Nagaoka–Hayashi bound. It was shown that the bound can be calculated via a semidefinite program.

Entanglement at the measurement stage (called collective measurements) can enhance multiparameter estimation precision by allowing joint measurements on multiple copies, thereby accessing a larger Hilbert space. However, determining and implementing optimal measurements utilising entanglement is a non-trivial task.