We address the problem of distributed quantum metrology with a single squeezed-vacuum source by using the formalism of quantum mechanics in phase space. In particular, we demonstrate Heisenberg-limited sensitivity in the measurement of the average of two arbitrary phase shifts in the arms of a Mach–Zehnder interferometer. We obtain exact results for the measurement probability at the interferometer output for any value of the phases, which give us insight into the emergence of Heisenberg-limited sensitivity for periodical values of the phases.
The canonical Mach-Zehnder interferometer fed with a coherent state and a squeezed-vacuum state of equal intensities is theoretically predicted to achieve Heisenberg scaling in phase sensitivity. However, this ultimate performance is unattainable using direct photon-number-difference detection due to a divergence arising precisely at the optimal equal-intensity regime. In this work, we introduce a dual-squeezing approach that overcomes this fundamental limitation. Our scheme employs an additional single-mode squeezer before detection, forming a paired configuration with the input squeezer used to generate the squeezed-vacuum state. We analytically demonstrate that the resulting dual-squeezing Mach-Zehnder interferometer enables Heisenberg-limited phase sensitivity with di rect photon-number-difference detection, while remaining robust against detection noise. Our work provides a feasible and robust route toward quantum-limited interferometric phase measurements
We study an entangled distributed quantum sensing scheme based on an array of
d Mach-Zehnder interferometers (MZIs) for the estimation of relative phase shifts. The scheme uses
d coherent states and a single squeezed-vacuum state that is distributed among the MZIs by a quantum circuit (QC). The protocol can be optimized analytically: it overcomes the shot-noise limit and reaches the Heisenberg limit with respect to the average total number of probe particles,
nT, for the estimation of arbitrary linear combinations of the
d phases. We compare the entangled strategy with a separable one that uses
d coherent and
d squeezed-vacuum states and the same
nT. The entangled strategy benefits for a substantial reduction of resource overhead and can achieve a maximum gain equal to
d when using the same total squeezed-light intensity as the separable strategy. Interestingly, the entangled strategy using a single squeezed-vacuum state can reach the same sensitivity as the separable strategy that uses
d copies of the same state. Finally, given a random choices of the QC, we identify the optimal linear combination of the phases that can be estimated with maximum sensitivity. Our scheme paves the ways for a variety of applications in distributed quantum sensing with photonic and atomic interferometers.
Achieving the ultimate quantum precision in the estimation of multiple physical parameters simultaneously is a challenge in quantum metrology due to fundamental limitations and experimental challenges in harnessing the necessary quantum resources. We propose an experimentally feasible scheme to reach Heisenberg-scaling precision in the simultaneous estimation of two unknown phase parameters in a Mach-Zehnder interferometer by using squeezed and coherent states of light as input and homodyne detections at the outputs. Our results open a new research paradigm in harnessing the full quantum advantage of multiparameter estimation in distributed quantum sensing and quantum information processing, as enabled by multiphoton quantum interference with scalable experimental resources.