Quantum sensing and quantum metrology propose schemes for the estimation of physical properties, such as lengths, time intervals, and temperatures, achieving enhanced levels of precision beyond the possibilities of classical strategies. However, such an enhanced sensitivity usually comes at a price: the use of probes in highly fragile states, the need to adaptively optimise the estimation schemes to the value of the unknown property we want to estimate, and the limited working range, are some examples of challenges which prevent quantum sensing protocols to be practical for applications. This work reviews two feasible estimation schemes which address these challenges, employing easily realisable resources, i.e., squeezed light, and achieve the desired quantum enhancement of the precision, namely the Heisenberg-scaling sensitivity. In more detail, it is here shown how to overcome, in the estimation of any parameter affecting in a distributed manner multiple components of an arbitrary M-channel linear optical network, the need to iteratively optimise the network. In particular, we show that this is possible with a single-step adaptation of the network based only on a prior knowledge of the parameter achievable through a “classical” shot-noise limited estimation strategy. Furthermore, homodyne measurements with only one detector allow us to achieve Heisenberg-limited estimation of the parameter. We further demonstrate that one can avoid the use of any auxiliary network at the price of simultaneously employing multiple detectors.
Quantum metrology enables parameter estimation beyond classical limits by exploiting nonclassical resources such as squeezing and entanglement. In distributed quantum sensing, Heisenberg scaling has been extended from
1/N2 to
1/(NM)2 through entanglement across both particles and spatial modes, where
N denotes the photon number and
M the number of spatially distributed modes. However, the overall sensitivity has remained limited to linear scaling with the number of measurement repetitions
R. Here, we show that exploiting entanglement across temporal modes via time-domain multiplexing enables a scaling advantage with respect to
R. As a result, the sensitivity can asymptotically approach simultaneous Heisenberg scaling in photons, spatial modes, and repetitions, yielding an overall sensitivity approaching
Δ2φ∝1/(NMR)2. Using the Bogoliubov transformation formalism, we prove the optimality of the protocol within the class of Gaussian states and show that the scaling is realizable via homodyne detection and maximum-likelihood estimation. We further show that the advantage persists under optical loss and propose an experimentally feasible loop-based photonic sensing scheme. Our results open a route to incorporating time-multiplexing techniques into quantum metrology.
We scrutinize the role of quantum entanglement in quantum metrology and discuss recent advances in nonlinear quantum metrology that allow improved scalings of the measurement precision with respect to the available resources. Such schemes can surpass the conventional Heisenberg limited scaling of 1/N of quantum enhanced metrology. Without investing in the preparation of entangled states, we review how systems with intrinsic nonlinearities such as Bose–Einstein condensates and light-matter interfaces can provide improved scaling in single parameter estimation.
We present a fully Gaussian and experimentally feasible scheme for the simultaneous estimation of the four real parameters that characterize a two-channel optical network. The scheme utilizes a two-mode squeezed probe and balanced homodyne detection at both output ports, for which we derive the complete classical Fisher information matrix analytically. Our scheme achieves the Heisenberg-scaling sensitivity for all four parameters simultaneously, enabling full multiparameter characterization of the two-channel interferometric network. We further show, by maximum-likelihood estimation, that the corresponding multiparameter Cramér-Rao bounds are saturated with a modest number of experimental repetitions and for low photon number. The scheme establishes a practical route to Heisenberg-scaling multiparameter Gaussian metrology for a two-channel network, with direct relevance to calibration and sensing in integrated photonics and distributed quantum-enhanced measurement architectures.