Quantum-enhanced strategies for surface and phase discrimination

Abstract

The ability to perform high precision measurements underpins a plethora of applications. Several techniques for force sensing, phase estimation and discrimination, as well as surface reconstruction for complex features of three-dimensional samples, have been developed in recent years. The main aim of this thesis is to investigate metrology enhancements due to quantum resources (probes and measurements), by using quantum parameter estimation and channel discrimination techniques. The thesis focuses on two main scenarios. In the first one, we deal with three-dimensional superlocalisation. By using tools from multiparameter quantum metrology, we show that a simultaneous estimation of all three components of the separation between two incoherent point sources in the paraxial approximation is achievable by a single quantum measurement, with a precision saturating the ultimate limit stemming from the quantum Cramér-Rao bound. Such a precision is not degraded in the sub-wavelength regime, thus overcoming the traditional limitations of classical direct imaging derived from Rayleigh's criterion. Our results are qualitatively independent of the point spread function of the imaging system, and quantitatively illustrated in detail for Gaussian beams. In this case, we show that a method of measuring the position of each photon at the imaging plane based on discrimination in terms of Hermite-Gaussian spatial modes reaches the quantum precision bound in the limit of infinitesimal separation. In the second part of the thesis, we investigate the role of quantum coherence as a resource for channel discrimination tasks. We consider a probe state of arbitrary dimension entering a black box, in which a phase shift is implemented, with the unknown phase randomly sampled from a finite set of predetermined possibilities. At the output, an optimal measurement is performed in order to guess which specific phase was applied in the process. We show that the presence of quantum coherence (superposition with respect to the eigenbasis of the generator of the phase shift) in the input probe directly determines an enhancement in the probability of success for this task, compared to the use of incoherent probes. We prove that such a quantum advantage is exactly quantified by the robustness of coherence, a full monotone with respect to the recently formulated resource theories of quantum coherence, whose properties and applications are developed and explored in detail