Quantum enhanced metrology: quantum mechanical correlations and uncertainty relations

The foundational theory of quantum enhanced metrology for parameter estimation is of fundamental importance to the progression of science and technology as the scientific method is built upon empirical evidence, the acquisition of which is entirely reliant on measurement. Quantum mechanical properties can be exploited to yield measurement results to a greater precision (lesser uncertainty) than that which is permitted by classical methods. This has been mathematically demonstrated by the derivation of theoretical bounds which place a fundamental limit on the uncertainty of a measurement. Furthermore, quantum metrology is of immediate interest in the application of quantum technologies since measurement plays a central role. This thesis focuses on the role of quantum correlations and uncertainty relations which govern the precision bounds. We show how correlations can be distributed amongst limited resources in realistic scenarios, as permitted by current experimental capabilities, to achieve higher precision measurements than current approaches. This is extended to the setting of multiparameter estimation in which we demonstrate a more technologically feasible method of correlation distribution than those previously posited which perform as well as, or worse than, our scheme. Furthermore, a quantum metrology protocol is typically comprised of three stages: probe state preparation, sensing and then readout, where the time required for the first and last stages is usually neglected. We consider the more realistic sensing scenario of time being a limited resource which is divided amongst the three stages and demonstrate the most efficient use of this resource. Additionally, we take an information theoretic approach to quantum mechanical uncertainty relations and derive a one-parameter class of uncertainty relations which supplies more information about the quantum mechanical system of interest than conventional uncertainty relations. Finally, we demonstrate how we can use this class of uncertainty relations to reconstruct information of the state of the quantum mechanical system.