Modern precision experiments often probe unknown classical fields with bosonic sensors in quantum-noise-limited regimes where vacuum fluctuations limit conventional readout. We introduce Quantum Signal Learning (QSL), a sensing framework that extends metrology to a broader property-learning setting, and propose a quantum-enhanced protocol that simultaneously estimates many properties of a classical signal with shot noise suppressed below the vacuum level. Our scheme requires only two-mode squeezing, passive optics, and static homodyne measurements, and enables post-hoc classical estimation of many properties from the same experimental dataset. We prove that our protocol enables a quantum speedup for common classical sensing tasks, including measuring electromagnetic correlations, real-time feedback control of interferometric cavities, and Fourier-domain matched filtering. To establish these separations, we introduce an optimal-transport conditioning method, and show both worst-case exponential separations from all entanglement-free strategies and practical speedups over homodyne and heterodyne baselines. We further show that when squeezing is treated as a resource, a protocol with squeezed light can sense a structured classical background exponentially faster than any coherent classical probe.
Modern precision experiments often probe unknown classical fields with bosonic sensors in quantum-noise-limited regimes where vacuum fluctuations limit conventional readout. We introduce Quantum Signal Learning (QSL), a sensing framework that extends metrology to a broader property-learning setting, and propose a quantum-enhanced protocol that simultaneously estimates many properties of a classical signal with shot noise suppressed below the vacuum level. Our scheme requires only two-mode squeezing, passive optics, and static homodyne measurements, and enables post-hoc classical estimation of many properties from the same experimental dataset. We prove that our protocol enables a quantum speedup for common classical sensing tasks, including measuring electromagnetic correlations, real-time feedback control of interferometric cavities, and Fourier-domain matched filtering. To establish these separations, we introduce an optimal-transport conditioning method, and show both worst-case exponential separations from all entanglement-free strategies and practical speedups over homodyne and heterodyne baselines. We further show that when squeezing is treated as a resource, a protocol with squeezed light can sense a structured classical background exponentially faster than any coherent classical probe.
Sensing time-varying signals is essential for precision measurement and for characterizing fluctuations in physical systems. In this work, we show that quantum entanglement provides an exponential advantage in the acquisition time required to learn the temporal statistics of a stationary classical signal. The task is to estimate the characteristic function of joint displacements on selected bosonic modes within a fixed-duration window, using continuous measurements of one signal realization. We present an entanglement-assisted scheme based on two-mode squeezed probes and local Bell measurements with protected idlers, and bound its acquisition time accounting for readout noise and correlations between signal windows. For a strictly stationary pulse family, it achieves polynomial acquisition time at inverse-polynomial accuracy with logarithmic squeezing and polynomial photon number. On the other hand, we prove that any local idler-free protocols require acquisition time exponential in the number of selected temporal modes per window. This lower bound holds for both sequentially prepared and arbitrarily temporally entangled probes, allowing non-Gaussian inputs and measurements and causal classical feedback, as long as each output is measured destructively within its time bin. These results establish an exponential quantum learning advantage for a single continuously monitored stationary signal, with the sensing cost measured by total acquisition time.
Quantum technology has the potential to transform scientific discovery, but quantum advantages often require processing capabilities well beyond the reach of experimental platforms. We show that coupling a single controllable qubit to an otherwise conventional sensor can exponentially reduce the number of measurements required to learn classical signals. These rigorous quantum advantages apply to fundamental sensing tasks, including learning Fourier coefficients, extracting temporal correlations from time-varying signals, and estimating transformations of physical observables. Using a superconducting cavity--qubit architecture, we experimentally demonstrate 107-fold reductions in the number of measurements required for Fourier-amplitude and time-varying signal learning. Our quantum feature sensing algorithms further enable orders-of-magnitude improvements in simulations of weak-signal dark matter detection and wireless communication applications. These quantum advantages are derived from Quantum Phase-Space Inference (QΨ), a unifying theory of quantum-enhanced experiments that simultaneously converts a set of experimental objectives and constraints into tight lower bounds and optimal quantum-enhanced learning algorithms while producing a certificate of quantum advantage. QΨ extends beyond the regimes captured by quantum Fisher information and provides a framework for systematically identifying rigorous quantum advantages in practical experimental tasks. Together, our results establish that near-term quantum technology can exponentially enhance our ability to learn from classical signals.
Quantum resources can dramatically reduce the data required to learn physical systems, with exponential improvements in sample complexity demonstrated in several quantum learning tasks. However, these advantages have typically relied on quantum resources that scale with problem complexity, most notably increasing system dimension or entanglement. This raises a fundamental question: can exponential quantum learning advantages arise within a fixed, unentangled quantum system? In this paper, we address this question by considering the learning of an unknown random-displacement distribution whose complexity is determined not by the dimensionality of the physical system, but by the Fourier resolution of its features. We show that the quantum-limited noise of vacuum probes progressively obscures high-frequency features, leading to an exponential growth in sample complexity. We establish an information-theoretic lower bound for arbitrary classical-state probes and show that squeezing overcomes this classical limit by extending the accessible Fourier bandwidth. Experimentally, we demonstrate an exponential reduction in sample complexity using squeezed vacuum probes for both binary hypothesis testing and characteristic-function reconstruction. Our results show that a single bosonic mode can exhibit exponential quantum learning advantages without entanglement or an increase in system size, identifying accessible Fourier bandwidth as a fundamentally distinct resource for quantum-enhanced learning.
Quantum light promises improved precision in optical remote sensing, but its practical advantage depends critically on whether nonclassical resources remain useful under realistic noise and experimentally accessible detection. This question becomes especially relevant for LiDAR systems, where a quantum advantage has been demonstrated for target detection and joint range-velocity estimation, but mostly under idealized conditions or simple noise models, such as optical loss and thermal background. A key open point is whether entanglement provides an operational advantage when the dominant disturbance is not independent noise, but structured interference across sensing modes. Here, we address this question by studying the joint estimation of target range and velocity with bright two-mode Gaussian probes and homodyne detection, comparing coherent, separable squeezed, and twin-beam states at a fixed resource budget. Our results reveal a hierarchy of quantum resources set by the noise structure: separable squeezing provides a robust advantage over coherent illumination under loss and thermal background, whereas twin-beam probes become superior under correlated jamming when the receiver is adaptively optimized. These results establish correlated noise as the operational regime in which entanglement provides a robustness advantage beyond local squeezing, opening a receiver-aware route to quantum-enhanced LiDAR in realistic and potentially adversarial environments.
Squeezed light enables quantum-enhanced phase estimation, with crucial applications in both fundamental physics and emerging technologies. To fully exploit the advantage provided by this approach, estimation protocols must remain optimal across the entire parameter range and resilient to instabilities in the probe state. In this context, strategies that rely on pre-calibrated squeezing levels are vulnerable to degradation over time and become sub-optimal when experimental conditions fluctuate. Here, we develop an adaptive multiparameter estimation strategy for ab-initio phase estimation, achieving sub-shot noise limit precision in the full periodicity interval [0, π), without relying on prior knowledge of the squeezing parameter. Our approach employs real-time feedback to jointly estimate both the optical phase and the squeezing level, ensuring robustness against experimental drifts and calibration errors. This self-calibrating scheme establishes a reliable quantum-enhanced sensing framework, opening new routes for practical scenarios and scalable distributed sensor networks using squeezed light.
Quantum sensing is an emerging field of quantum optics that seeks to take advantage of quantum correlations available in quantum states of light to enable sensitivities beyond the fundamental classical limits. \nThe sensitivity of measurements and sensing apparatus when using classical states of light is limited to the shot-noise limit (SNL), which is achieved with coherent states of light. \n \nTwo-mode squeezed states of light (twin beams) have quantum correlations both in time and space, leading to temporal and spatial squeezing properties. \nSeveral applications can benefit from such noise reduction to enable new approaches, such as quantum-enhanced interferometry, quantum imaging, and quantum sensing. \nThe emergence of quantum technologies has been referred to as the second quantum revolution. \nFor metrology and sensing applications, in particular, it has led to new state-of-the-art sensitivity limits. \n \nIn this thesis, we discuss the implementation of quantum sensing based on squeezed states of light and plasmonic sensors as a platform for the demonstration of real-life quantum sensing. \nWe present a quantum-enhanced plasmonic sensing setup that can detect changes in the refractive index of air beyond the SNL. \nFurthermore, we generalize such experimental apparatus to probe an array of sensors using the quantum correlations present in different spatial locations to demonstrate a parallel quantum-enhanced plasmonic sensing scheme that can simultaneously detect changes in the refractive index of air in multiple locations with a single probing beam. \nThese results prove the applicability of twin beams for real-life applications based on plasmonic sensors. \nThe spatially resolved sensing scheme can be extended to pixel-size sensing of multiple sensors for multi-parameter estimation and detection applications to reach more complex sensing architectures.