Quantum metrology enables sensitivity to approach the limits set by fundamental physical laws. Even a single continuous mode offers enhanced precision, with the improvement scaling with its occupation number. Due to their high information capacity, continuous modes allow for the engineering of quantum non-Gaussian states, which not only improve metrological performance but can also be tailored to specific experimental platforms and conditions. Recent advancements in control over continuous platforms operating in the quantum regime have renewed interest in sensing weak forces, also coupling to massive macroscopic objects. In this work, we investigate a force-sensing scheme where a physical process completely randomizes the direction of the induced phase-space displacement, and the unknown force strength is inferred through excitation-number-resolving measurements. We find that N-spaced states, where only every N^{th} Fock state occupation is nonzero, approach the achievable sensing bound. Additionally, non-Gaussian states are shown to be more resilient against decoherence than their Gaussian counterparts with the same occupation number. While Fock states typically offer the best protection against decoherence, we uncover a transition in the metrological landscape-revealed through a tailored decoherence-aware Fisher-information-based reward functional-where experimental constraints favor a family of number-squeezed Schrödinger cat states. Specifically, by implementing quantum optimal control in a minimal spin-boson system, we identify these states as maximizing force sensitivity under lossy dynamics and finite system controllability. Our results provide a pathway for enhancing force sensing in a variety of continuous quantum systems, ranging from massive systems like mechanical oscillators to massless systems such as quantum light and microwave resonators.
As one of the main pillars of quantum technologies, quantum metrology aims to improve measurement precision using techniques from quantum information. The two main strategies to achieve this are the preparation of nonclassical states and the design of optimized measurement observables. We discuss precision limits and optimal strategies in quantum metrology and sensing with a single mode of quantum continuous variables. We focus on the practically most relevant cases of estimating displacements and rotations and provide the sensitivities of the most important classes of states that includes Gaussian states and superpositions of Fock states or coherent states. Fundamental precision limits that are obtained from the quantum Fisher information are compared to the precision of a simple moment-based estimation strategy based on the data obtained from possibly sub-optimal measurement observables, including homodyne, photon number, parity and higher moments. Finally, we summarize some of the main experimental achievements and present emerging platforms for continuous-variable sensing. These results are of particular interest for experiments with quantum light, trapped ions, mechanical oscillators, and microwave resonators.
Massive mechanical oscillators couple directly to forces, accelerations and gravity, making them attractive probes of new physics and of quantum mechanics at macroscopic scales. Pushing sensitivities beyond the standard quantum limit for signals of unknown phase requires non-Gaussian quantum states, whose metrological advantage has so far been confined to lighter systems such as trapped ions. Here we operate a microgram-scale acoustic mode of a high-overtone bulk acoustic wave resonator as a phase-insensitive quantum-enhanced sensor. A transmon qubit prepares the mode in Fock states of up to seven phonons by optimal control, and resolves its phonon-number distribution after interaction with a weak resonant signal. Bayesian analysis yields a Fisher information five times the vacuum value, a 7.0 dB gain in signal-amplitude sensitivity over any classical probe state, irrespective of its energy, currently limited by state preparation infidelities. We then train a neural network on the measured sensor response to perform Bayesian estimation without any analytical model of the system, showing the same sensitivity gain with half the systematic bias. Our results establish acoustic resonators prepared in non-Gaussian states as quantum-enhanced probes for high-frequency gravitational waves, dark matter and wave-function collapse.
Distributed quantum sensing leverages quantum correlations among multiple sensors to enhance the precision of parameter estimation beyond classical limits. Most existing approaches target phase estimation and rely on a shared phase reference between the signal and the probe, yet many relevant scenarios deal with regimes where such a reference is absent, making the estimation of force or field amplitudes the main task. We study this phase-insensitive regime for bosonic sensors that undergo identical displacements with common phases randomly varying between experimental runs. We derive analytical bounds on the achievable precision and show that it is determined by first-order normal correlations between modes in the probe state, constrained by their average excitations. These correlations yield a collective sensitivity enhancement over the standard quantum limit, with a gain that grows linearly in the total excitation number, revealing a distributed quantum advantage even without a global phase reference. We identify families of multimode states with definite joint parity that saturate this limit and can be probed efficiently via local parity measurements already demonstrated or emerging in several quantum platforms. We further demonstrate that experimentally relevant decoherence channels favor two distinct sensing strategies: splitting of a single-mode nonclassical state among the modes, which is robust to loss and heating, and separable probes, which are instead resilient to dephasing and phase jitter. Our results are relevant to multimode continuous platforms, including trapped-ion, solid-state mechanical, optomechanical, superconducting, and photonic systems.
Fock states of the quantum harmonic oscillator are fundamental to quantum sensing and information processing, serving as key resources for exploiting bosonic degrees of freedom. Here, we prepare high Fock states in a high-overtone bulk acoustic wave resonator by coupling it to a superconducting qubit and applying microwave pulses designed using quantum optimal control. We characterize the experimentally realized states by employing a criterion for genuine quantum non-Gaussianity (QNG) designed to reveal multiphonon contributions. Although energy relaxation and decoherence limit the achievable fidelities, we demonstrate genuine QNG features compatible with a Fock state |6⟩, confirming that the prepared states cannot be generated through Gaussian operations on states with up to Fock state |5⟩ contributions. We further investigate the robustness of these QNG features to losses and their utility in sensing displacement amplitudes. In particular, we introduce a hierarchy based on the quantum Fisher information and show that, despite decoherence and measurement imperfections, the prepared states achieve a displacement sensitivity surpassing that of an ideal Fock state |3⟩. Our results have immediate applications in quantum sensing and simulations with high-overtone bulk acoustic wave resonator devices.
Cubic phase states provide the essential non-Gaussian resource for continuous-variable quantum computing. We show that they also offer significant potential for quantum metrology, surpassing the phase-sensing sensitivity of all Gaussian states at equal average photon number. Optimal sensitivity requires only moderate initial squeezing, and the non-Gaussian advantage remains robust against loss and detection noise. We identify optimal measurement strategies and show that several experimentally relevant preparation schemes surpass Gaussian limits, in some cases reaching the sensitivity of cubic phase states. Our results establish cubic phase states as a promising resource for quantum-enhanced precision measurements beyond Gaussian limits.
Quantum noise limits high-precision sensing, such as in gravitational wave detectors. Caves first proposed beating this shot-noise limit by injecting squeezed vacuum at the dark port of an interferometer. Frequency-dependent squeezing through a filter cavity now delivers broadband quantum noise reductions of up to 5.2 dB at Hanford and 6.1 dB at Livingston in the LIGO detectors' fourth observing run. Building on these advances, this thesis develops techniques for interferometric sensing under realistic loss and phase noise, spanning Gaussian state preparation, optomechanical readout and feedback control, and non-Gaussian state preparation. In Parts I and II, we work in the two-photon formalism, where states are Gaussian and dynamics are linear. In Part I, we present a waveguide squeezer as an alternative to the traditional bulk cavity-based source; it is single-pass, broadband, and compact, and its modularity opens a path to non-Gaussian state generation. We report the detection of squeezed light from waveguide sources at 1064 nm in the sub-MHz regime, and we phase-stabilize the squeezed vacuum with quantum noise locking. We also analyze the loss and phase-noise tolerance of Gaussian states. In Part II, we design a tabletop phase-sensitive optomechanical amplifier and analyze its performance in terms of cavity stability, control system, and noise budget. We then implement the locking scheme, including Pound-Drever-Hall locking of the cavity, and characterize the noise budget at the initial stage. We also propose using optomechanics for coherent feedback control, which could evade back-action and broaden the detection bandwidth of future gravitational wave detectors. In Part III, we turn to non-Gaussian states. Phase noise does not preserve Gaussianity, so the best input state under combined loss and phase noise need not be Gaussian. We numerically optimize the input state for displacement sensing over the
(η,σϕ) landscape, integrating the Lindblad master equation in a truncated Fock basis and computing the quantum Fisher information. Within the Gaussian sub-family, the optimizer returns a displaced squeezed state once phase noise is appreciable, rather than pure squeezed vacuum. Without the Gaussian restriction, the optimized states sort roughly into four classes (Fock-like, cubic-phase-like, discrete-rotational, and squeezed), each dominant in a different region of the parameter space. In the experimentally relevant region of 1% loss and 100 mrad phase noise, cat states outperform squeezed vacuum even with balanced homodyne readout, an improvement implementable in the near term. We also show that the non-Gaussian advantage persists at higher photon budgets, well above
Nˉ=5. Together, these results show how state preparation, readout, and feedback choices trade off against realistic loss and phase noise, and identify the regimes where non-Gaussian states perform better.