# Entangling measurements for multiparameter estimation with two qubits

## TL;DR

This paper explores how entangling measurements on two qubits can improve the simultaneous estimation of certain parameters, like phase and phase diffusion, in quantum sensing, with experimental validation in photonics.

## Contribution

It demonstrates that entangling measurements on two qubits enhance joint estimation of phase and phase diffusion, revealing limitations for multiple phases.

## Key findings

- Entangling measurements improve phase and phase diffusion estimation.
- No enhancement observed for multiple phases.
- Experimental validation in photonics setup.

## Abstract

Careful tailoring the quantum state of probes offers the capability of investigating matter at unprecedented precisions. Rarely, however, the interaction with the sample is fully encompassed by a single parameter, and the information contained in the probe needs to be partitioned on multiple parameters. There exist then practical bounds on the ultimate joint-estimation precision set by the unavailability of a single optimal measurement for all parameters. Here we discuss how these considerations are modified for two-level quantum probes - qubits - by the use of two copies and entangling measurements. We find that the joint estimation of phase and phase diffusion benefits from such collective measurement, while for multiple phases, no enhancement can be observed. We demonstrate this in a proof-of-principle photonics setup.