Quantum sensing with many-body systems

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.