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Quantum Sensing of Curvature

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Abstract

We address the problem of sensing the curvature of a manifold by performing measurements on a particle constrained to the manifold itself. In particular, we consider situations where the dynamics of the particle is quantum mechanical and the manifold is a surface embedded in the three-dimensional Euclidean space. We exploit ideas and tools from quantum estimation theory to quantify the amount of information encoded into a state of the particle, and to seek for optimal probing schemes, able to actually extract this information. Explicit results are found for a free probing particle and in the presence of a magnetic field. We also address precision achievable by position measurement, and show that it provides a nearly optimal detection scheme, at least to estimate the radius of a sphere or a cylinder.

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Acknowledgements

This work has been supported by SERB through project VJR/2017/000011. MGAP is member of GNFM-INdAM.

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Authors and Affiliations

  1. Quantum Technology Lab, Dipartimento di Fisica Aldo Pontremoli, Università degli Studi di Milano, I-20133, Milano, Italy

    Daniele Bonalda, Luigi Seveso & Matteo G. A. Paris

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  1. Daniele Bonalda
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  2. Luigi Seveso
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  3. Matteo G. A. Paris
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Correspondence to Matteo G. A. Paris.

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Bonalda, D., Seveso, L. & Paris, M.G.A. Quantum Sensing of Curvature. Int J Theor Phys 58, 2914–2935 (2019). https://doi.org/10.1007/s10773-019-04174-9

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  • DOI: https://doi.org/10.1007/s10773-019-04174-9

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