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Distributed quantum metrology (DQM) enables the estimation of global functions of d distributed parameters beyond the capability of separable sensors. Continuous-variable DQM involves using a linear network with at least one nonclassical input. Here, we fully elucidate the structure of linear networks with two nonvacuum inputs, which allows us to prove a number of fundamental properties of continuousvariable DQM. While measuring the sum of d parameters at the Heisenberg limit can be achieved with a single nonvacuum input, we show that two inputs, one of which can be classical, are required to measure an arbitrary linear combination of d parameters and an arbitrary global function of the parameters. We obtain a universal and tight upper bound on the sensitivity of DQM networks with two inputs, and completely characterize the properties of the nonclassical input required to obtain a quantum advantage. This reveals that a wide range of nonclassical states makes this possible, including a squeezed vacuum. We also show that, for a class of nonclassical inputs, local photon number detection will achieve the maximum sensitivity. Finally we show that a general DQM network has two distinct regimes. The first achieves Heisenberg scaling. In the second the nonclassical input is much weaker than the coherent input, nevertheless providing a multiplicative enhancement to the otherwise classical sensitivity. 

We present a cavity-enhanced solid-state nuclear spin gyroscope based on nitrogen-vacancy centers in diamond. With the two-field interference, we indicate a state-of-the-art rotation sensitivity and pave the way for advancements in high-performance quantum sensing. 

Abstract Quantum sensors based on solid-state defects, in particular nitrogen-vacancy (NV) centers in diamond, enable precise measurement of magnetic fields, temperature, rotation, and electric fields. Cavity quantum electrodynamic (cQED) readout, in which an NV ensemble is hybridized with a microwave mode, can overcome limitations in optical spin detection and has resulted in leading magnetic sensitivities at the pT-level. This approach, however, remains far from the intrinsic spin-projection noise limit due to thermal Johnson-Nyquist noise and spin saturation effects. Here we tackle these challenges by combining recently demonstrated spin refrigeration techniques with comprehensive nonlinear modeling of the cQED sensor operation. We demonstrate that the optically-polarized NV ensemble simultaneously provides magnetic sensitivity and acts as a heat sink for the deleterious thermal microwave noise background, even when actively probed by a microwave field. Optimizing the NV-cQED system, we demonstrate a broadband sensitivity of 576 ± 6 fT/$$\sqrt{{{{\rm{Hz}}}}}$$ $\sqrt{\mathrm{Hz}}$ around 15 kHz in ambient conditions. We then discuss the implications of this approach for the design of future magnetometers, including near-projection-limited devices approaching 3 fT/$$\sqrt{{{{\rm{Hz}}}}}$$ $\sqrt{\mathrm{Hz}}$ sensitivity enabled by spin refrigeration. 

Abstract It is well-known that the precision of a phase measurement with a Mach-Zehnder interferometer employing strong classic light can be greatly enhanced with the addition of weak nonclassical light. In the context of quantifying nonclassicality, the amount by which a nonclassical state can enhance precision in this way has been termed its ’metrological power’. To-date, the enhancement provided by weak nonclassical states has been calculated only for specific measurement configurations. Here we are able to optimize over all measurement configurations to obtain the maximum enhancement that can be achieved by any single or multi-mode nonclassical state together with strong classical states, for local and distributed quantum metrology employing any linear or nonlinear single-mode unitary transformation. Our analysis reveals that the quantum Fisher information for quadrature-displacement sensing is the sole property that determines the maximum achievable enhancement in all of these different scenarios, providing a unified quantification of the metrological power.