Optimal function estimation with photonic quantum sensor networks
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866913274347388928 |
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| author | Bringewatt, Jacob Ehrenberg, Adam Goel, Tarushii Gorshkov, Alexey V. |
| author_facet | Bringewatt, Jacob Ehrenberg, Adam Goel, Tarushii Gorshkov, Alexey V. |
| contents | The problem of optimally measuring an analytic function of unknown local parameters each linearly coupled to a qubit sensor is well understood, with applications ranging from field interpolation to noise characterization. Here, we resolve a number of open questions that arise when extending this framework to Mach-Zehnder interferometers and quadrature displacement sensing. In particular, we derive lower bounds on the achievable mean square error in estimating a linear function of either local phase shifts or quadrature displacements. In the case of local phase shifts, these results prove, and somewhat generalize, a conjecture by Proctor et al. [arXiv:1702.04271 (2017)]. For quadrature displacements, we extend proofs of lower bounds to the case of arbitrary linear functions. We provide optimal protocols achieving these bounds up to small (multiplicative) constants and describe an algebraic approach to deriving new optimal protocols, possibly subject to additional constraints. Using this approach, we prove necessary conditions for the amount of entanglement needed for any optimal protocol for both local phase and displacement sensing. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_16472 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Optimal function estimation with photonic quantum sensor networks Bringewatt, Jacob Ehrenberg, Adam Goel, Tarushii Gorshkov, Alexey V. Quantum Physics The problem of optimally measuring an analytic function of unknown local parameters each linearly coupled to a qubit sensor is well understood, with applications ranging from field interpolation to noise characterization. Here, we resolve a number of open questions that arise when extending this framework to Mach-Zehnder interferometers and quadrature displacement sensing. In particular, we derive lower bounds on the achievable mean square error in estimating a linear function of either local phase shifts or quadrature displacements. In the case of local phase shifts, these results prove, and somewhat generalize, a conjecture by Proctor et al. [arXiv:1702.04271 (2017)]. For quadrature displacements, we extend proofs of lower bounds to the case of arbitrary linear functions. We provide optimal protocols achieving these bounds up to small (multiplicative) constants and describe an algebraic approach to deriving new optimal protocols, possibly subject to additional constraints. Using this approach, we prove necessary conditions for the amount of entanglement needed for any optimal protocol for both local phase and displacement sensing. |
| title | Optimal function estimation with photonic quantum sensor networks |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2401.16472 |