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Quantum metrology in the presence of limited data

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journal contribution
posted on 2023-06-09, 17:01 authored by Jesus Rubio Jimenez, Jacob DunninghamJacob Dunningham
Quantum metrology protocols are typically designed around the assumption that we have an abundance of measurement data, but recent practical applications are increasingly driving interest in cases with very limited data. In this regime the best approach involves an interesting interplay between the amount of data and the prior information. Here we propose a new way of optimising these schemes based on the practically-motivated assumption that we have a sequence of identical and independent measurements. For a given probe state we take our measurement to be the best one for a single shot and we use this sequentially to study the performance of different practical states in a Mach-Zehnder interferometer when we have moderate prior knowledge of the underlying parameter. We find that we recover the quantum Cramér-Rao bound asymptotically, but for low data counts we find a completely different structure. Despite the fact that intra-mode correlations are known to be the key to increasing the asymptotic precision, we find evidence that these could be detrimental in the low data regime and that entanglement between the paths of the interferometer may play a more important role. Finally, we analyse how close realistic measurements can get to the bound and find that measuring quadratures can improve upon counting photons, though both strategies converge asymptotically. These results may prove to be important in the development of quantum enhanced metrology applications where practical considerations mean that we are limited to a small number of trials.

Funding

UK Quantum Technology Hub: NQIT-Networked Quantum Information Technologies; G1503; EPSRC-ENGINEERING & PHYSICAL SCIENCES RESEARCH COUNCIL; EP/M013243/1

History

Publication status

  • Published

File Version

  • Accepted version

Journal

New Journal of Physics

ISSN

1367-2630

Publisher

Institute of Physics

Department affiliated with

  • Physics and Astronomy Publications

Research groups affiliated with

  • Atomic, Molecular and Optical Physics Research Group Publications

Full text available

  • Yes

Peer reviewed?

  • Yes

Legacy Posted Date

2019-02-28

First Open Access (FOA) Date

2019-02-28

First Compliant Deposit (FCD) Date

2019-02-28

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