Distributed Quantum Multiparameter Estimation with Optimal Local Measurements

Year: 2025

Authors: Pezzè L., Smerzi A.

Autors Affiliation: Consiglio Nazl Ric CNR, Ist Nazl Ott, Largo Enrico Fermi 6, I-50125 Florence, Italy; European Lab Nonlinear Spect LENS, Via N Carrara 1, I-50019 Sesto Fiorentino, Italy.

Abstract: We study the multiparameter sensitivity bounds of a network of d spatially distributed Mach-Zehnder interferometers (MZIs). A generic single nonclassical state is mixed with d – 1 vacuums to create a d-mode 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 Cramer-Rao bound. The sensor network can overcome the shot noise limit for the estimation of arbitrary linear combinations of the d phase shifts, provided that the nonclassical probe state has an antisqueezed 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 d nonclassical states rather than a single one. Considering the same average number of particles per shot in the two protocols, nT, we find analytically a sensitivity scaling 1=n2T for the entangled case that provides a gain factor d with respect to the separable case where the sensitivity scales as d=n2T. We have numerical evidence that the gain factor d is also found when fixing the total average number of particles, namely when optimizing with respect to the number of repeated measurements.

Journal/Review: PHYSICAL REVIEW LETTERS

Volume: 135 (26)      Pages from: 260805-1  to: 260805-7

More Information: We acknowledge discussions with M. Malitesta at an early stage of this work, and with A. Datta and R. Demkowicz-Dobrza n ski. This publication has received funding under Horizon Europe programme HORIZON-CL4-2022-QUANTUM-02-SGA via the Project No. 101113690 (PASQuanS2.1) . L. P. acknowl-edges financial support by the QuantEra project SQUEIS. This research was supported in part by the Grant No. NSF PHY-1748958 to the Kavli Institute for Theoretical Physics (KITP) .
KeyWords: Average numbers; Coherent state; Gain factors; Input port; Local measurement; Mach-Zehnder; Mode entangled state; Multiparameters; Nonclassical state; Zehnder interferometers
DOI: 10.1103/f2jf-bg7g