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.
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.
We provide the optimal measurement strategy for a class of noisy channels that reduce to the identity channel for a specific value of a parameter (spreading channels). We provide an example that is physically relevant: the estimation of the absolute value of the displacement in the presence of phase randomizing noise. Surprisingly, this noise does not affect the effectiveness of the optimal measurement. We show that, for small displacement, a squeezed vacuum probe field is optimal among strategies with same average energy. A squeezer followed by photodetection is the optimal detection strategy that attains the quantum Fisher information, whereas the customarily used homodyne detection becomes useless in the limit of small displacements, due to the same effect that gives Rayleigh's curse in optical superresolution. There is a quantum advantage: a squeezed or a Fock state with N average photons allow to asymptotically estimate the parameter with a sqrt[N] better precision than classical states with same energy.
Quantum metrology aims to achieve measurement precision that surpasses classical limits in the estimation of physical parameters. In realistic conditions, however, its advantage can be diminished by interactions between a quantum system and its environment. This necessitates careful design of quantum resources that can sustain enhanced performance even under noise. Here, we investigate how a quantum non-Gaussian operation can provide an advantage in noisy quantum metrology. Specifically, we examine the effect of single-photon subtraction applied to a two-mode squeezed vacuum state in the task of phase estimation using a Mach–Zehnder interferometer under photon loss. The single-photon subtraction can be implemented either before or after the first beam splitter in the interferometer. By evaluating the quantum Fisher information for both the original and the photon-subtracted states, we assess the potential enhancement in sensing precision. We show that the enhancement occurs when photon subtraction is performed before the first beam splitter, provided that loss acts only on the signal mode. Our findings shed light on the role of non-Gaussian operations in noisy quantum metrology, clarifying when photon subtraction can yield a genuine advantage over Gaussian resources.
The modern scientific method is critically dependent on precision measurements of physical parameters. A classic example is the measurement of the optical phase enabled by optical interferometry, where the error on the measured phase is conventionally bounded by the so-called Heisenberg limit. To achieve phase estimation at the Heisenberg limit, it has been common to consider protocols based on highly complex N00N states of light. However, despite decades of research and several experimental explorations, there has been no demonstration of deterministic phase estimation with N00N states reaching the Heisenberg limit or even surpassing the shot noise limit. Here we use a deterministic phase estimation scheme based on a source of Gaussian squeezed vacuum states and high-efficiency homodyne detection to obtain phase estimates with an extreme sensitivity that significantly surpasses the shot noise limit and even beats the conventional Heisenberg limit as well as the performance of a pure N00N state protocol. Using a high-efficiency setup with a total loss of about 11%, we achieve a Fisher information of 15.8(6) rad^{-2} per photon-a significant increase in performance compared to state of the art and beyond an ideal six photon N00N state scheme. This work represents an important achievement in quantum metrology, and it opens the door to future quantum sensing technologies for the interrogation of light-sensitive biological systems.
Abstract We propose a photon subtraction scheme within the Mach–Zehnder interferometer using a coherent state and a squeezed vacuum state as inputs. By systematically comparing intensity detection and homodyne detection methods, we demonstrate that strategically applied photon subtraction ( a -mode subtraction) significantly enhances the phase sensitivity of all detection methods. Under this configuration, homodyne detection achieves superior phase sensitivity and loss robustness compared to intensity detection. Remarkably, under 30% photon loss, the system surpasses the Heisenberg limit, enabled by the synergy among the squeezed vacuum state, non-Gaussian operations, and detection optimization. Furthermore, we quantify performance through the quantum Fisher information and the quantum Cramér-Rao bound analyses under both ideal and lossy conditions.