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Quantum sensing networks for the estimation of linear functions

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Version 1 2023-06-09, 21:42
journal contribution
posted on 2023-06-12, 09:30 authored by Jesús Rubio, Paul A Knott, Timothy J Proctor, Jacob DunninghamJacob Dunningham
The theoretical framework for networked quantum sensing has been developed to a great extent in the past few years, but there are still a number of open questions. Among these, a problem of great significance, both fundamentally and for constructing efficient sensing networks, is that of the role of inter-sensor correlations in the simultaneous estimation of multiple linear functions, where the latter are taken over a collection local parameters and can thus be seen as global properties. In this work we provide a solution to this when each node is a qubit and the state of the network is sensor-symmetric. First we derive a general expression linking the amount of inter-sensor correlations and the geometry of the vectors associated with the functions, such that the asymptotic error is optimal. Using this we show that if the vectors are clustered around two special subspaces, then the optimum is achieved when the correlation strength approaches its extreme values, while there is a monotonic transition between such extremes for any other geometry. Furthermore, we demonstrate that entanglement can be detrimental for estimating non-trivial global properties, and that sometimes it is in fact irrelevant. Finally, we perform a non-asymptotic analysis of these results using a Bayesian approach, finding that the amount of correlations needed to enhance the precision crucially depends on the number of measurement data. Our results will serve as a basis to investigate how to harness correlations in networks of quantum sensors operating both in and out of the asymptotic regime.

History

Publication status

  • Published

File Version

  • Published version

Journal

Journal of Physics A: Mathematical and General

ISSN

0305-4470

Publisher

IOP Publishing

Issue

34

Volume

53

Page range

1-28

Article number

a344001

Department affiliated with

  • Physics and Astronomy Publications

Research groups affiliated with

  • Sussex Centre for Quantum Technologies Publications

Full text available

  • Yes

Peer reviewed?

  • Yes

Legacy Posted Date

2020-09-28

First Open Access (FOA) Date

2020-09-28

First Compliant Deposit (FCD) Date

2020-09-26

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