Quantum imaging in the near and far field: an estimation theory analysis

In this thesis, we propose a model for quantum imaging. A general imaging setup is represented as a quantum Gaussian channel consisting of three key steps: diffraction through an object, modeled as a parametric family of beam splitters where the parameter encodes crucial information about the object's geometry; propagation through free space, described using classical optical transfer functions, allowing analysis under both far field and near field conditions; detection with a finite-size detector, also modeled as a family of beam splitters parametrized by the detector's spatial extension. A central focus of quantum imaging is achieving superresolution, the ability to resolve features smaller than the classical diffraction limit. This is often studied within the framework of quantum metrology by comparing the classical and quantum Fisher information associated with the parameter, which typically represents the separation between two apertures in an otherwise opaque object. Following this approach, we compute these key quantities for several analytically tractable states, such as coherent states and single-photon states, commonly used in quantum optics. Finally, we explore an alternative perspective on superresolution based on the framework of classical and quantum statistical hypothesis testing, taking preliminary steps to investigate the minimum probability of distinguishing a single-aperture geometry from a double-aperture geometry.