Distributed quantum multiparameter estimation with optimal local measurements

• URL: http://arxiv.org/abs/2405.18404v1
• Date: Tue, 28 May 2024 17:45:07 GMT
• Title: Distributed quantum multiparameter estimation with optimal local measurements
• Authors: Luca Pezzè, Augusto Smerzi,
• Abstract summary: We study a sensor made by an array of $d$ spatially-distributed Mach-Zehnder interferometers (MZIs) We show that local measurements, independently performed on each MZI, are sufficient to provide a sensitivity saturating the quantum Cram'er-Rao bound. We find that the $d$ independent interferometers can achieve the same sensitivity of the entangled protocol but at the cost of using additional $d$ non-classical states.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We study the multiparameter sensitivity bounds of a sensor made by an array of $d$ spatially-distributed Mach-Zehnder interferometers (MZIs). A generic single non-classical state is mixed with $d-1$ vacuums to create a $d$-modes entangled state, each mode entering one input port of a MZI, while a coherent state enters its second port. We show that local measurements, independently performed on each MZI, are sufficient to provide a sensitivity saturating the quantum Cram\'er-Rao bound. The sensor can overcome the shot noise limit for the estimation of arbitrary linear combinations of the $d$ phase shifts, provided that the non-classical probe state has an anti-squeezed quadrature variance. We compare the sensitivity bounds of this sensor with that achievable with $d$ independent MZIs, each probed with a nonclassical state and a coherent state. We find that the $d$ independent interferometers can achieve the same sensitivity of the entangled protocol but at the cost of using additional $d$ non-classical states rather than a single one. When using in the two protocols the same average number of particles per shot $\bar{n}_T$, we find analytically a sensitivity scaling $1/\bar{n}_T^2$ for the entangled case which provides a gain factor $d$ with respect to the separable case where the sensitivity scales as $d/\bar{n}_T^2$. We have numerical evidences that the gain factor $d$ is also obtained when fixing the total average number of particles, namely when optimizing with respect to the number of repeated measurements.

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