Curator's Take
AI Commentary
This thesis delivers a much‑needed unified language for describing how the modal structure, state statistics and symmetry constraints of light translate into usable quantum resources, bridging the gap between abstract photonic theory and concrete hardware designs. By treating time–frequency degrees of freedom as continuous variables and clarifying their entanglement properties, it directly supports current efforts in frequency‑bin qubits, integrated photonic processors, and ultra‑precise interferometric sensors that aim to hit Heisenberg‑limited performance. The symmetry‑based formalism also highlights the practical impact of optical superselection rules, warning engineers that certain state preparations may be fundamentally inaccessible without additional resources.
— Mark Eatherly
Summary
This thesis explores the role of modes, states, and symmetries in quantum optics, within the context of quantum information and quantum metrology. It proposes a unified framework to analyze how the modal structure of photonic fields, the statistical nature of states, and their symmetry properties determine the physical resources that can be exploited for quantum information processing and quantum parameter estimation. A first line of investigation develops a description of time-frequency degrees of freedom as continuous quantum variables, highlighting their richness for encoding and manipulating information. A second axis studies entanglement and collective variables, clarifying the link between physical resources and metrological gains, particularly in reaching ultimate precision limits. Interferometric scenarios of the Hong-Ou-Mandel type are then analyzed, and a general formalism centered on the notion of symmetry is developed. This framework enables the analysis of a broad range of situations and leads to several generalizations. Finally, the thesis examines the symmetries imposed by optical superselection rules and their consequences for the structure of quantum states and their operational performance, with the aim of providing a deeper understanding of the foundations of quantum optics.