26th Australian Institute of Physics Congress and the Australian and New Zealand Conference on Optics and Photonics

Trade-offs and entanglement in quantum multiparameter estimation

Not scheduled

20m

Belinda Hutchinson Building (The University of Sydney )

Invited talk AIP | Quantum Science and Technology (QST)

Speaker

Simon Yung (Australian National University)

Description

Quantum estimation theory provides the basis for quantum metrology. However, quantum multiparameter estimation is fundamentally limited by the uncertainty principle. This manifests as a trade-off between attainable estimation precisions, because the optimal measurements for each parameter are generally incompatible. Using quantum Cramér–Rao bounds, we analysed these trade-offs and compared them to existing results [1]. Specialising to two parameters, we investigated when it is possible to attain the fundamental precision limit for one parameter while still obtaining information about the other [2]. Dubbed “prioritised estimation”, this is practically useful when one parameter is of interest while another encodes noise but nevertheless needs to be estimated. We also determined a simple expression for the fundamental limit for two-parameter estimation with pure states and the corresponding optimal measurement [3]. This result applies straightforwardly even in continuous-variable systems; as an example, we determined the fundamental limit to sensing orthogonal displacements using grid states.

Quantum mechanics also offers a tool that helps mitigate the trade-off imposed by the uncertainty principle: entanglement. Measurement precision can be improved by using entanglement to perform joint measurements on multiple copies of a quantum state. The enhancement extends to the estimation of more than two parameters, which can be assessed by extending the Cramér–Rao bound analysis. As a practical example, we studied qubit tomography by estimating the components of a qubit’s Bloch vector. We determined the optimal two-copy measurements that saturate the trade-off limit and demonstrated these with a proof-of-principle experiment on a photonic platform [4]. These results can be generalised to other physical systems to investigate their potential for quantum-enhanced metrology.

[1]: S. K. Yung et al., Physical Review Research 6, 033315
[2]: S. K. Yung et al., arXiv:2511.06704
[3]: S. K. Yung et al., Physical Review Applied (https://doi.org/10.1103/2nx2-k97n)
[4]: S. K. Yung, W.-Z. Yan, et al., arXiv:2604.08871