2024/05/28 by Pezzè, Luca, Smerzi, Augusto · 4 citations
#FOS: Physical sciences #Quantum Physics (quant-ph)
paper · doi:10.48550/arxiv.2405.18404
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 Cramér-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 nT, we find analytically a sensitivity scaling 1/nT2 for the entangled case which provides a gain factor d with respect to the separable case where the sensitivity scales as d/nT2. 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.