Quantum systems used for metrology can offer enhanced precision over their classical counterparts. The design of quantum sensors can be optimized by maximizing the quantum Fisher information (QFI), which characterizes the precision of parameter estimation for an ideal measurement. Here we consider the response of a quantum system as a means to estimate the strength of a weak external perturbation. General expressions for the QFI in the nonequilibrium steady-state are derived, which hold for arbitrary interacting many-body systems at finite or zero temperature, and can be related to susceptibilities or linear-response transport coefficients. For quantum dot nanoelectronics devices, we show that electron interactions can lead to *exponential* scaling of the QFI with system size, highlighting that quantum resources can be utilized in the full Fock space. The precision estimation of voltages and fields can also be achieved by practical measurements. In particular, we show that current-based metrology in quantum circuits can leverage many-body effects for enhanced sensing.
Quantum systems used for metrology can offer enhanced precision over their classical counterparts. The design of quantum sensors can be optimized by maximizing the quantum Fisher information (QFI), which characterizes the precision of parameter estimation for an ideal measurement. Here we consider the response of a quantum system as a means to estimate the strength of a weak external perturbation. General expressions for the QFI in the nonequilibrium steady-state are derived, which hold for arbitrary interacting many-body systems at finite or zero temperature, and can be related to susceptibilities or linear-response transport coefficients. For quantum dot nanoelectronics devices, we show that electron interactions can lead to exponential scaling of the QFI with system size, highlighting that quantum resources can be utilized in the full Fock space. The precision estimation of voltages and fields can also be achieved by practical measurements. In particular, we show that current-based metrology in quantum circuits can leverage many-body effects for enhanced sensing.
Fundamental scientific advances are often facilitated by breakthroughs in calibration and readout techniques that increase the measurement precision of sensors. The betterment of sensing technologies enables the validation of existing scientific theories and congruently, may also pave the way for identifying breakdowns in these frameworks, signalling the necessity for new theoretical developments. A significant facet of the growing interest in quantum metrology is that it represents a prime example in which quantum features such as entanglement, squeezing, and criticality, can be harnessed to enhance the precision of parameter estimation well beyond the capacity of their classical counterparts. We begin by exploring the paradigmatic problem of temperature estimation using impurity probes embedded in a host environment. The physical setup considered provides a natural mechanism for the probe-environment unit to equilibrate and thermalize. Furthermore the nature of probe-environment interactions allows us to investigate the role that entanglement plays in equilibrium temperature estimation problems. Our analysis reveal that spectral features of the environment are imprinted on the probe system due to established entanglement and uncover a low temperature regime with a universal thermometric response that is independent of the microscopic details of the environment. Physical incarnations of nanoelectronic devices are operated in the linear-response regime with transport properties representing the measurement of choice. Motivated by this, we next propose nanoelectronic devices operated in this way as a novel paradigm for quantum sensing. We derive general expressions for the quantum Fisher information --- allowing us to provide a precision benchmark for quantum transport coefficients in the linear-response regime. The latter half of this thesis is concerned with aspects of quantum critical metrology and multiparameter estimation. Our first contribution is to propose an alternative platform for critical quantum metrology, the two-impurity Kondo model --- which does not rely on the preparation of exotic critical states, but instead can be passively tuned to criticality. Employing local measurements of the in situ probe at finite temperature, we find enhanced precision at criticality in estimating inter-impurity coupling, but low precision when utilized as a thermometer. Considering uncertainty in both of these parameters, we find the quantum Fisher information matrix to be singular, despite these parameters being physically independent. We demonstrate that application of a known control field can lift the singularity. In practical settings, an external parameter is tuned to bring a system to its quantum critical point. Therefore, we expect that experimental uncertainties in this control parameter to play a significant role in fully exploiting criticality as a resource for sensing. Motivated by this, we next propose a general framework interpolating between the single and multi-parameter settings. Applied to the Ising and Lipkin-Meshkov-Glick models, we establish a fundamental trade-off between the amount of uncertainty a critical system can withstand while still maintaining a quantum advantage for sensing. In the final chapter of the thesis, we investigate the physical origin of quantum fisher information matrix singularities. A singularity signals a fundamental breakdown in our ability to estimate parameters and bound their precision. We attribute these situations to emergent metrological symmetries whereby the same set of measurement outcomes are obtained for different combinations of the system parameters. We demonstrate that by using Bayesian estimation, deep insights can be revealed and estimation of effective parameters is possible by employing a parameter transformation of the Bayesian posterior distribution.
We develop a quantum metrological framework for resonant nanophotonic sensors based on subwavelength Fabry--Perot slit cavities. Building on classical Fisher-information analyses of resonant transmission sensors, we model parameter encoding as a phase-and-loss quantum channel embedded in one arm of a Mach-Zehnder interferometer. We derive the quantum Fisher information (QFI) for coherent and Gaussian probe states under linear loss and show that, even at the quantum limit, optimal estimation precision is governed by the generator of parameter-dependent phase shifts rather than by the cavity quality factor. Consequently, the operating point that maximizes the QFI does not generally coincide with the maximum-Q resonance. Quantum resources enhance sensitivity but do not redefine the optimal geometry. Our results provide physically transparent design principles for quantum-enhanced nanophotonic sensing.
Quantum-enhanced sensing is commonly benchmarked using the quantum Fisher information (QFI), often interpreted as a direct indicator of achievable precision. However, such an interpreta- tion is only justified within a fully specified inference framework that consistently incorporates state preparation, measurement design, resource accounting, estimator construction, prior information, and finite data effects. Here we develop an operational, end-to-end framework for quantum sensing under finite resources and identify general principles required for meaningful performance assess- ment. A central conceptual point is that the relevant unit of estimation is not a single detection event, but the complete data set required to construct a consistent estimator. Rather than relying on abstract statistical formalism, we analyze a set of paradigmatic and experimentally relevant ex- amples that expose common pitfalls in widely discussed quantum sensing strategies. These include quantum interferometry, sensing with squeezed states, and criticality-inspired protocols. Our results clarify when large Fisher information or nonclassical resources translate into genuine metrological advantage, and when they do not. They further provide a practical methodology for designing and evaluating quantum sensing protocols under realistic experimental constraints.
We develop a quantum metrological framework for resonant nanophotonic sensors based on subwavelength Fabry-Perot (FP) slit cavities. Building directly on classical Fisher-information analyses of resonant transmission sensors, we model parameter encoding as a phase-and-loss quantum channel embedded in one arm of a Mach-Zehnder interferometer. We derive the quantum Fisher information (QFI) for coherent and Gaussian probe states under linear loss and show that, even at the quantum limit, optimal estimation precision is governed by the generator of parameter-dependent phase shifts-dominated by interface contributions-rather than by the cavity quality factor. Consequently, the operating point that maximizes QFI does not generally coincide with the maximum-Q resonance. Quantum resources enhance sensitivity but do not redefine the optimal geometry. Our results provide physically transparent design principles for quantum-enhanced nanophotonic sensing and clarify the central role of boundaries and loss in quantum-limited precision.
Quantum Fisher information (QFI) determines the ultimate precision of a quantum sensor after optimization over all allowed measurements, but it does not quantify how difficult the optimal readout is to implement. We introduce a moment Fisher hierarchy FM(k), which measures the fraction of QFI accessible to collective spin moments up to degree k, together with a readout-complexity scale k90 defined by the minimum degree required to recover 90% of the QFI. Applying this framework to a nonlinear collective-spin sensor, we show that many-body dynamics can preserve large QFI while transferring the optimal readout into high-rank SU(2) tensor sectors inaccessible to low-order collective observables. For system sizes up to N=100, first moments access only ∼10−2 of the available QFI, while the degree required to recover 90% of it grows to k90≃28. A rank-resolved analysis of the symmetric logarithmic derivative (SLD) under weak damping shows that the nonlinear protocol pushes the optimal readout toward the highest available tensor ranks while strongly depleting its low-rank weight. These results identify nonlinear tangent-space shear as the mechanism behind a finite-size readout-complexity bottleneck in many-body quantum metrology.
We study the phenomenon of quantum synchronization from the viewpoint of quantum metrology. By interpreting quantum self-sustained oscillators as dissipative quantum sensors, we develop a framework to characterize several aspects of quantum synchronization. We show that the quantum Fisher information (QFI) serves as a system-agnostic measure of quantum synchronization that also carries a clear operational meaning, viz., it quantifies the precision with which the amplitude of a weak synchronizing drive can be measured. We extend our analysis to study many-body oscillators subjected to multiple drives. We show how the QFI matrix can be used to determine the optimal drive that maximizes quantum synchronization, and also to quantitatively differentiate the synchronization responses induced by different drives. Our work highlights multiple connections between quantum synchronization and quantum metrology, paving a route toward finding quantum technological applications of quantum synchronization.