Continuous monitoring of open quantum-optical systems offers a promising route towards quantum-enhanced sensing. In such sensing schemes, the ultimate precision limit is dictated by the quantum Cramér-Rao bound. However, reaching this fundamental bound with established continuous measurement techniques has remained an outstanding challenge. Here, we present an approach tailored to open quantum-optical sensors operating near dissipative critical points. The key insight of our approach is to exploit a synergy between the intrinsic critical dynamics and the unavoidable quantum measurement backaction of continuous homodyne detection. By carefully aligning the homodyne phase to the squeezing angle of the sensor state, quantum backaction can be evaded in the critical dynamics, thereby significantly boosting the attainable precision. We demonstrate the broad applicability of this approach across several sensor models and for both single- and multi-parameter estimation, showing that it consistently narrows the gap toward the ultimate precision bound.
Continuous monitoring of open quantum-optical systems offers a promising route towards quantum-enhanced sensing. In such sensing schemes, the ultimate precision limit is dictated by the quantum Cramér-Rao bound. However, reaching this fundamental bound with established continuous measurement techniques has remained an outstanding challenge. Here, we present an approach tailored to open quantum-optical sensors operating near dissipative critical points. The key insight of our approach is to exploit a synergy between the intrinsic critical dynamics and the unavoidable quantum measurement backaction of continuous homodyne detection. By carefully aligning the homodyne phase to the squeezing angle of the sensor state, quantum backaction can be evaded in the critical dynamics, thereby significantly boosting the attainable precision. We demonstrate the broad applicability of this approach across several sensor models and for both single- and multi-parameter estimation, showing that it consistently narrows the gap toward the ultimate precision bound.
Dissipative phase transitions in the driven-dissipative Kerr parametric oscillator offer a promising route for realizing criticality-enhanced quantum sensing based on continuous measurements. However, achieving such enhancement through realistic measurement schemes remains an outstanding challenge. Here, we extend the backaction-evasion strategy introduced in our earlier work for the Gaussian linear case [arXiv:2511.22248 (2025)] to analyze how the quantum and classical Fisher information scale with the Kerr nonlinearity at dissipative critical points. Our results show that backaction-evading homodyne monitoring achieves enhanced photon-number scaling that surpasses the standard quantum limit, and significantly outperforms alternative protocols such as continuous photon counting. As an additional methodological contribution, we also implement and benchmark time-discrete approximation schemes with improved statistical convergence properties. We use these methods to compute the classical Fisher information for continuous homodyne detection, and demonstrate that they provide efficient access to this quantity near dissipative critical points, thereby extending the reach of existing methods.
Quantum sensors hold considerable promise for precision measurement, yet their capabilities are inherently constrained by environmental noise. A fundamental task in quantum sensing is determining the precision limit of noisy sensor devices. For continuously monitored quantum sensors, characterizing the optimal precision in the presence of environments other than the measurement channel is an outstanding open theoretical challenge, due to the infinite-dimensional nature of the sensor output field and the complex temporal correlation of the photons therein. Here, we establish a numerically efficient method to determine the quantum Cramér-Rao bound for continuously monitored quantum sensors subject to general environmental noise-Markovian or non-Markovian, and showcase its application with paradigmatic models of continuously monitored quantum sensors. Applicable to both constant-parameter and waveform estimation, our method provides a rigorous and practical framework for assessing and enhancing the sensor performance in realistic settings, with broad applications across experimental quantum physics.
Continuous monitoring of driven-dissipative quantum optical systems is a crucial element in the implementation of quantum metrology, providing essential strategies for achieving highly precise measurements beyond the classical limit. In this context, the relevant figure of merit is the quantum Fisher information of the radiation field emitted by the driven-dissipative sensor. Saturation of the corresponding precision limit as defined by the quantum Cramer-Rao bound is typically not achieved by conventional, temporally local continuous measurement schemes such as counting or homodyning. To address the outstanding open challenge of efficient retrieval of the quantum Fisher information of the emission field, we design a novel continuous measurement strategy featuring temporally quasilocal measurement bases as captured by matrix product states. Such measurement can be implemented effectively by injecting the emission field of the sensor into an auxiliary open system, a `quantum decoder' module, which `decodes' specific input matrix product states into simple product states as its output field, and performing conventional continuous measurement at the output. We devise a universal recipe for the construction of the decoder by exploiting time reversal transformation of quantum optical input-output channels, thereby establishing a universal method to achieve the quantum Cramer-Rao precision limit for generic sensors based on continuous measurement. As a by-product, we establish an effective formula for the evaluation of the quantum Fisher information of the emission field of generic driven-dissipative open sensors. We illustrate the power of our scheme with paramagnetic open sensor designs including linear force sensors, fibre-interfaced nonlinear emitters, and driven-dissipative many-body sensors, and demonstrate that it can be robustly implemented under realistic experimental imperfections.
Continuous monitoring of driven-dissipative quantum-optical systems is a crucial element in the implementation of quantum metrology, providing essential strategies for achieving highly precise measurements beyond the classical limit.In this context, the relevant figure of merit is the quantum Fisher information of the radiation field emitted by the driven-dissipative sensor.Saturation of the corresponding precision limit as defined by the quantum Cramér-Rao bound is typically not achieved by conventional, temporally local continuous-measurement schemes such as counting or homodyning.To address the outstanding open challenge of efficient retrieval of the quantum Fisher information of the emission field, we design a novel continuous-measurement strategy featuring temporally quasilocal measurement bases as captured by matrix-product states.Such a measurement can be implemented effectively by injecting the emission field of the sensor into an auxiliary open system, a "quantum-decoder" module, which "decodes" specific input matrix-product states into simple product states as its output field, and performing conventional continuous measurement at the output.We devise a universal recipe for the construction of the decoder by exploiting the time-reversal transformation of quantum-optical input-output channels, thereby establishing a universal method to achieve the quantum Cramér-Rao precision limit for generic sensor designs based on continuous measurement.As a by-product, we establish an effective formula for the evaluation of the quantum Fisher information of the emission field of generic drivendissipative open sensors.We illustrate the power of our scheme with paramagnetic open sensor designs including linear force sensors, fiber-interfaced nonlinear emitters, and driven-dissipative many-body sensors, and demonstrate that it can be robustly implemented under realistic experimental imperfections.
Fast and precise characterization of Gaussian states is crucial for their effective use in quantum technologies. In this work, we apply a multiparameter moment-based estimation method that enables rapid and accurate determination of squeezing, antisqueezing, and the squeezing angle of the squeezed vacuum state. Compared to conventional approaches, our method achieves faster parameter estimation with reduced uncertainty, reaching the Cramér-Rao bound. We validate its effectiveness using the two most common measurement schemes in continuous-variable quantum optics: homodyne detection and double homodyne detection. This rapid estimation framework is well suited for dynamically characterizing sources with time-dependent parameters, potentially enabling real-time feedback stabilization.
The backaction of quantum measurements is traditionally regarded as an unavoidable source of noise that limits the precision of state estimation and control. In this work we propose a novel conceptual framework, the Quantum Measurement Backaction Topology (QMBT), in which the measurement backaction is understood as possessing a topological structure. We introduce the notion of a measurement backaction manifold T_M, defined by the set of all possible dynamical trajectories induced by continuous measurements. By mapping the evolution of the density matrix under measurement to a geometrical flow on T_M, we identify conserved quantities and topological invariants that constrain the backaction dynamics. The QMBT formalism is formulated using stochastic master equations with measurement operators M_k and corresponding noise terms, and we show that the resulting equations can be cast into a form reminiscent of gauge theories on fiber bundles. This perspective allows us to classify measurement protocols according to their topological class and to predict robustness against parameter variations. We illustrate the theory with continuous monitoring of a two–level system and a bosonic mode, demonstrating how the topology dictates the long–time behavior of the system and the achievable measurement precision. The QMBT framework opens a pathway to modify quantum measurement theory fundamentally, potentially enabling the design of measurement schemes that evade the traditional noise floor and thereby unlocking new regimes of quantum control and metrology.