In optical interferometry path-entangled states such as NOON states have shown to give quantum-enhanced precision measurements, but these states are notoriously fragile to particle losses, which typically collapse the quantum state and destroy the phase information. A class of inherently robust states that show the potential for great improvements over the alternatives are the entangled coherent states (ECSs). We show that these states allow substantial improvements over unentangled `classical' states and highly-entangled NOON states for a wide range of loss values. We then describe a measurement scheme that can be used to measure these states with a precision close to the theoretical bound given by the quantum Fisher information.
We then look at the quantum mechanisms that lead to precise measurements. In optical interferometry multi-mode entanglement is often assumed to be the driving force behind quantum enhanced measurements. Recent work has shown this assumption to be false, and here we show that when photon losses occur multi-mode entanglement is actually detrimental to obtaining quantum enhanced measurements. We specifically apply this idea to a superposition of coherent states, demonstrating that these states show a robustness to loss that allows them to significantly outperform their competitors in realistic systems. A practically viable measurement scheme is then presented that allows measurements close to the theoretical bound, even with loss.
In this thesis we also consider superpositions of spin coherent states and their application to quantum metrology. Compared to optical states, spin systems have a distinctly different process of decoherence known as non-Markovian dephasing, which has shown to give greatly improved robustness to loss. We see that spin cat states give an enhanced scaling over the shot noise limit, even with dephasing, whilst being realisable with current technology
