Quanta emitted by an open quantum system carry information about intrinsic parameters, enabling their estimation via continuous monitoring. In practice, however, only a fraction of the emitted quanta is detected, reducing the achievable sensitivity. Here, we consider few-level systems in which coherent couplings and dissipative processes compete, producing metastable dynamics characterized by emission intermittency or by the emergence of a dark state. We show that both phenomena can be beneficial for sensing but their relative performance depends strongly on the achievable detection efficiencies. Intermittent emission, marked by long alternating bright and dark periods, allows to achieve robustness with respect to inefficient detection and dephasing, whereas dark states yield significantly higher sensitivity at unit detection efficiency. Yet the latter are highly susceptible to losses. We quantify the impact of inefficient detection through the classical Fisher information of the emission record and benchmark it against the ultimate sensitivity encoded in the joint system-environment state. Finally, we demonstrate that maximum-likelihood estimators based on the observed emission record can effectively approach this sensitivity. We focus here on trapped-ion systems, however, the results extend to other quantum platforms in which similar emission dynamics can be observed.
Quanta emitted by an open quantum system carry information about intrinsic parameters, enabling their estimation via continuous monitoring. In practice, however, only a fraction of the emitted quanta is detected, reducing the achievable sensitivity. Here, we consider few-level systems in which coherent couplings and dissipative processes compete, producing metastable dynamics characterized by emission intermittency or by the emergence of a dark state. We show that both phenomena can be beneficial for sensing but their relative performance depends strongly on the achievable detection efficiencies. Intermittent emission, marked by long alternating bright and dark periods, allows to achieve robustness with respect to inefficient detection and dephasing, whereas dark states yield significantly higher sensitivity at unit detection efficiency. Yet the latter are highly susceptible to losses. We quantify the impact of inefficient detection through the classical Fisher information of the emission record and benchmark it against the ultimate sensitivity encoded in the joint system-environment state. Finally, we demonstrate that maximum-likelihood estimators based on the observed emission record can effectively approach this sensitivity. We focus here on trapped-ion systems, however, the results extend to other quantum platforms in which similar emission dynamics can be observed.
Quantum continuous measurement strategies are an essential element in many modern sensing technologies, leading to potentially enhanced estimation of unknown physical parameters. In such schemes, continuous monitoring of the quantum system, which encodes the parameters of interest, gives rise to different quantum trajectories conditioned on the measurement outcomes which carry information on the parameters themselves. Importantly, different trajectories carry different amounts of information, i.e., they are more or less sensitive to the unknown parameters of interest. In this work, we propose an approach on how to systematically engineer the quantum open-system dynamics in order to increase the probability of obtaining trajectories of high sensitivity. We focus on the simplest case scenario of a single two-level system interacting with ancillas, which are in turn measured using the discretized version of continuous monitoring. We analyze the performance of our protocol and demonstrate that it may lead to a substantial enhancement of sensitivity, as quantified by the classical Fisher information, even when applied to such small system sizes, holding the promise of direct implementation in state-of-the-art experimental platforms and large, complex many-body systems.
Quantum systems in nonequilibrium conditions, where coherent many-body interactions compete with dissipative effects, can feature rich phase diagrams and emergent critical behavior. Associated collective effects, together with the continuous observation of quanta dissipated into the environment-typically photons-allow one to achieve quantum-enhanced parameter estimation. However, protocols for tapping this enhancement typically involve intricate measurements on the combined system-environment state. Here, we show that many-body quantum enhancement can in fact be obtained through classical measurements such as photon counting and homodyne detection. We illustrate this in detail for a class of open spin-boson models, which can be realized in trapped-ion or cavity QED setups. Our findings highlight a route toward the design of systems that enable a practical implementation of quantum-enhanced metrology through continuous classical measurements.
In this thesis we explore aspects of dynamics of open quantum systems related to coherence and quantum correlations - necessary resources for enhanced quantum metrology and quantum computation. We first discuss limits to the precision of parameter estimation when using a quantum system in the presence of noise. To this end we introduce a variational principle for the quantum Fisher information (QFI) bounding the estimation errors of any measurement, which motivates an efficient iterative algorithm for finding optimal system preparations for noisy estimation experiments. Furthermore, we investigate influence of noise correlations on the precision in phase and frequency estimation, by delivering bounds for both spatially and temporarily correlated (non-Markovian) dephasing noise. This allows us to prove the Zeno limit in frequency estimation, conjectured in Phys. Rev. A 84, 012103 (2011) and Phys. Rev. Lett. 109, 233601 (2012). The enhanced estimation precision in quantum metrology can be, however, achieved only using highly entangled states. We propose a scheme of generating such highly correlated states as outputs of Markovian open quantum systems near first-order dynamical phase transitions. We show that the quadratic scaling of the QFI with time is present for experiments within the correlation time of the dynamics and describe a theoretical scheme for quantum enhanced estimation of an optical phase-shift using the photons being emitted from an intermittent quantum system. Finally, we establish the basis for a theory of metastability in Markovian open quantum systems, by extending methods from classical stochastic dynamics. We argue that the partial relaxation into long-lived metastable states - distinct from the asymptotic stationary state - may preserve initial coherences within decoherence-free subspaces or noiseless subsystems, thus allowing for quantum computation during the metastable regime.
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.
This study investigates quantum-enhanced parameter estimation through continuous monitoring in open quantum systems that exhibit a dissipative time crystal phase. We first analytically derive the global quantum Fisher information (QFI) rate for boundary time crystals (BTCs), demonstrating that within the time-crystal phase, the ultimate precision exhibits a cubic scaling with the system size, fglobal∼N3. We then generalize this finding to a broader class of dynamics, including the transverse collective dephasing (TCD) model, which achieves a time-crystal phase through a closing Liouvillian gap without requiring a dissipative phase transition. We proceed to numerically demonstrate that this maximal global QFI rate is experimentally attainable for both the BTC and TCD models, even at finite system sizes, via continuous homodyne and photodetection. Moving towards practical implementations, we analyze the precision limits under inefficient detection, revealing a critical difference: for BTC dynamics, inefficiencies asymptotically restore a classical scaling, and only a constant-factor quantum advantage remains possible. In contrast, for TCD dynamics, a super-classical scaling is still in principle observable, and our numerical simulations confirm its presence, even under inefficient measurement conditions, establishing the TCD model as a highly robust platform for quantum metrology.
Continuous quantum metrology holds promise for realizing high-precision sensing by harnessing information progressively carried away by the radiation quanta emitted into the environment. Despite recent progress, a comprehensive understanding of the precision limits of continuous metrology with bosonic systems is currently lacking. We develop a general theoretical framework for quantum metrology with multimode free bosons under continuous Gaussian measurements. We derive analytical expressions for the asymptotic growth rates of the global quantum Fisher information (QFI) and the environmental QFI, which quantify the total information encoded in the joint system-environment state and the information accessible from the emitted radiation, respectively. We show that the asymptotic growth rates of the global and environmental QFIs coincide in a class of continuous sensing protocols with dissipative system-environment couplings, while they are in general qualitatively distinct when a system-environment coupling exhibits no damping. We further derive bounds on these quantities, showing that while a quadratic scaling with the number of modes is attainable, the precision scales at most linearly with time and a meaningful energy resource. To illustrate our findings, we analyze several concrete setups, including coupled cavity arrays and trapped particle arrays. While a local setup yields a linear scaling with resources, a globally coupled setup can achieve a quadratic scaling in terms of the mode number. Furthermore, we demonstrate that a nonreciprocal setup can leverage the non-Hermitian skin effect to realize an exponentially enhanced global QFI. Notably, however, this enhancement cannot be reflected in the environmental QFI, highlighting a fundamental distinction between the information stored within the joint state and the information radiated into the environment. ...