Localization-delocalization transitions have recently been proposed for building a class of efficient quantum many-body critical sensors. This work scrutinizes metrological performances of such devices by focusing on the Aubry-André-Harper model that supports a localization-delocalization transition at finite strength of the onsite potential. We identify a metrological quantum-to-classical crossover driven by the interplay between noise and system size, whereby quantum-enhanced scaling of the quantum Fisher information persists only up to a finite, noise-dependent characteristic system-size. We first consider thermal noise and show that, at and near the localization-delocalization transition, the quantum Fisher information exhibits quantum-enhanced scaling for small systems but the system is stripped of this advantage beyond the characteristic crossover length. The crossover length decreases with increasing temperature. We then consider imperfections in the lattice hopping strengths and find a qualitatively similar crossover. There, the quantum-enhanced regime, identified with super-extensive scaling, gives way to an extensive scaling-a classical-limited weaker form-at sufficiently large system sizes. Thus, distinct noise mechanisms lead to a common limitation on the scalability of quantum-enhanced sensing: increasing the probe size beyond a noise-dependent limit can destroy the metrological quantum advantage.
Localization-delocalization transitions have recently been proposed for building a class of efficient quantum many-body critical sensors. This work scrutinizes metrological performances of such devices by focusing on the Aubry-André-Harper model that supports a localization-delocalization transition at finite strength of the onsite potential. We identify a metrological quantum-to-classical crossover driven by the interplay between noise and system size, whereby quantum-enhanced scaling of the quantum Fisher information persists only up to a finite, noise-dependent characteristic system-size. We first consider thermal noise and show that, at and near the localization-delocalization transition, the quantum Fisher information exhibits quantum-enhanced scaling for small systems but the system is stripped of this advantage beyond the characteristic crossover length. The crossover length decreases with increasing temperature. We then consider imperfections in the lattice hopping strengths and find a qualitatively similar crossover. There, the quantum-enhanced regime, identified with super-extensive scaling, gives way to an extensive scaling-a classical-limited weaker form-at sufficiently large system sizes. Thus, distinct noise mechanisms lead to a common limitation on the scalability of quantum-enhanced sensing: increasing the probe size beyond a noise-dependent limit can destroy the metrological quantum advantage.
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.
Quantum metrology shows that by exploiting nonclassical resources it is possible to overcome the fundamental limit of precision found for classical parameter-estimation protocols. The scaling of the quantum Fisher information -- which provides an upper bound to the achievable precision -- with respect to the protocol duration is then of primarily importance to assess its performances. In classical protocols the quantum Fisher information scales linearly with time, while typical quantum-enhanced strategies achieve a quadratic (Heisenberg) or even higher-order polynomial scalings. Here we report a protocol that is capable of surpassing the polynomial scaling, and yields an exponential advantage. Such exponential advantage is achieved by approaching, but without crossing, the critical point of a quantum phase transition of a fully-connected model in the thermodynamic limit. The exponential advantage stems from the breakdown of the adiabatic condition close to a critical point. As we demonstrate, this exponential scaling is well captured by the new bound derived in arXiv:2110.04144, which in turn allows us to obtain approximate analytical expressions for the quantum Fisher information that agree with exact numerical simulations. In addition, we discuss the limitations to the exponential scaling when considering a finite-size system as well as its robustness against decoherence effects. Hence, our findings unveil a novel quantum metrological protocol whose precision scaling goes beyond the paradigmatic Heisenberg limit with respect to the protocol duration.
Critical quantum metrology exploits the dramatic growth of the quantum Fisher information near quantum phase transitions to enhance the precision of parameter estimation. This enhancement is commonly associated with a closing energy gap, which causes the characteristic timescales for adiabatic preparation or relaxation to diverge with increasing system size. As a consequence, the apparent growth of the quantum Fisher information largely reflects the increasing evolution time induced by critical slowing down rather than a genuine improvement in metrological performance, thereby limiting the practical usefulness of such protocols. Here we show that the relationship between energy gaps, quantum correlations, and achievable precision in interacting quantum systems can be far more subtle. In particular, quantum-enhanced sensitivity can also emerge when the energy gap increases, eliminating critical slowing down and enabling substantially faster relaxation dynamics. Although the corresponding quantum Fisher information may decrease due to the shorter evolution time, the resulting precision can nevertheless remain quantum-enhanced. Building on this insight, we introduce an anti-critical quantum metrology scheme in which quantum-enhanced precision arises while the energy gap grows. We illustrate this mechanism using the quantum Rabi model, thereby identifying a route to metrological advantage that avoids the slow dynamics associated with conventional criticality.
Many-body localization (MBL) provides a mechanism by which interacting quantum systems evade thermalization, leading to persistent memory of initial conditions and slow entanglement growth. Probing these dynamical signatures in large systems and at long evolution times remains challenging for both classical simulations and current quantum devices. Here we experimentally investigate the ergodic-MBL crossover in quasiperiodic Floquet Ising systems using up to 144 qubits on an IBM Quantum processor. By implementing deep Floquet circuits reaching up to 5000 cycles, we access long-time many-body dynamics beyond the regime explored in previous quantum computing experiments. Measurements of autocorrelation functions reveal a smooth crossover from rapid thermalization at weak quasiperiodic potential strength to persistent correlations in the strong-disorder regime. Notably, in addition to the one-dimensional system, we also observe clear signatures consistent with localization behavior in the two-dimensional system. Furthermore, the quantum Fisher information exhibits logarithmic growth over thousands of Floquet cycles, providing evidence for slow entanglement spreading characteristic of the MBL regime. These results demonstrate that programmable quantum processors can serve as experimental platforms for probing nonergodic quantum many-body dynamics and exploring localization phenomena in regimes beyond the reach of classical simulations.
We investigate the sensing capacity of non-equilibrium dynamics in quantum systems exhibiting Bloch oscillations. By focusing on the resource efficiency of the probe, quantified by quantum Fisher information, we find different scaling behaviors in two different phases, namely localized and extended. Our results provide a quantitative ansatz for quantum Fisher information in terms of time, probe size, and the number of excitations. In the long-time regime, the quantum Fisher information is a quadratic function of time, touching the Heisenberg limit. The system size scaling drastically depends on the phase changing from quantum-enhanced scaling in the extended phase to size-independent behavior in the localized phase. Furthermore, increasing the number of excitations always enhances the precision of the probe, although, in the interacting systems the enhancement becomes less eminent than the non-interacting probes. This is due to the induced localization by increasing the interaction between the excitations. We show that a simple particle configuration measurement together with a maximum likelihood estimation can closely reach the ultimate precision limit in both single- and multi-particle probes.
Critical properties of a quantum system are recognized as valuable resources for quantum metrology. In this work, we investigate the criticality-enhanced sensing in a quantum Rabi triangle system, which exhibits multiple phases. Around the phase boundary, enhanced parameter estimation precision can be achieved by tuning either the scaled coupling strength or the hopping phase controlled by an artificial magnetic field. We observe that the quantum Fisher information shows divergent scaling near different quantum phase transition points, characterized by distinct critical exponents. When the resource consumption is taken into account, we find that the divergent quantum Fisher information can reach the Heisenberg limit. Furthermore, we propose a measurement scheme of the average photon number and the quantum Cramér-Rao bound can be saturated.