Quantum Multiparameter Estimation: Exploring Fundamental Limits and Testing Quantum Mechanics

Abstract

Quantum mechanics simultaneously offers unique opportunities for, and identifies restrictions on, the measurement of physical quantities. On one hand, the field of quantum metrology leverages quantum resources to enhance the accuracy of measurements. On the other hand, the uncertainty principle, a cornerstone of quantum mechanics, states that noncommuting observables cannot be simultaneously measured with an arbitrary accuracy. Quantum multiparameter estimation sits at the interface of these conflicting viewpoints; utilising quantum resources to overcome the inherent incompatibility of measuring multiple different observables. This thesis investigates the fundamental limits of quantum multiparameter estimation and its applications. We begin by introducing the Nagaoka-Hayashi bound, which sets limits on the precision attainable when estimating multiple parameters with separable, non-entangling, measurements. This contrasts with the most widely used bound in quantum metrology, the Holevo Cramer-Rao bound, which can be reached when using entangling measurements on infinitely many copies of the probe state. Using the Nagaoka-Hayashi Cramer-Rao bound, we show that the Holevo Cramer-Rao bound cannot be saturated in many physically relevant scenarios, raising questions as to its utility. Next, we develop and implement a measurement which entangles two copies of a quantum system. With this, we surpass the separable measurement limit and saturate, for the first time, the theoretical limit for entangling measurements on two copies of the quantum system. The measurement we develop also has major implications for the uncertainty principle. With this measurement, we violate uncertainty relations previously thought to be "universally valid". We then apply the techniques developed to probe fundamental aspects of quantum information. We first experimentally demonstrate that entangling measurements can help distinguish between two non-orthogonal quantum states. Secondly, using Cramer-Rao bounds we theoretically and experimentally map a quantum metrology task to secure quantum communication. Finally, we develop and demonstrate a novel measurement for testing the postulates of quantum mechanics. Show more