Interfacing Continuous and Discrete Hilbert Spaces in Quantum Optics and Quantum Information

My doctoral thesis details my research on two major projects. Both projects investigate the correspondence between the discrete (photon number) and the continuous (quadrature) representation of optical states. Understanding the relationships between the two representations is very important for the investigation of quantum physics phenomena. Moreover it has significant applications in quantum computing where it is found that discrete-variable bases are easier to error-correct but some continuous-variable architectures are more scalable. Research in the connection between the two representation might help develop new architectures for scalable fault-tolerant quantum computing.