Quantum sensing networks for the estimation of linear functions

Rubio, Jesús, Knott, Paul A, Proctor, Timothy J and Dunningham, Jacob A (2020) Quantum sensing networks for the estimation of linear functions. Journal of Physics A: Mathematical and General, 53 (34). a344001 1-28. ISSN 0305-4470

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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.

Item Type: Article
Keywords: quantum sensing networks, multi-parameter estimation, quantum metrology, quantum correlations
Schools and Departments: School of Mathematical and Physical Sciences > Physics and Astronomy
Research Centres and Groups: Sussex Centre for Quantum Technologies
Subjects: Q Science > QC Physics > QC0170 Atomic physics. Constitution and properties of matter Including molecular physics, relativity, quantum theory, and solid state physics > QC0174.12 Quantum theory. Quantum mechanics
Depositing User: Jacob Dunningham
Date Deposited: 28 Sep 2020 10:53
Last Modified: 28 Sep 2020 11:00
URI: http://sro.sussex.ac.uk/id/eprint/94015

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