Measurement-Based non-Gaussian Quantum State Engineering

Advances in quantum technologies promise to deliver a great deal of progress in information science, including applications in sensing, secure communication, and quantum computation. If successfully implemented, an error-corrected universal quantum computer would deliver an exponential boost in efficiency when solving certain problems. However, this requires a way to generate and entangle many low-noise quantum resources in a scalable way. Fortunately, quantum computing with the continuous-variable nature of light in a quantum-optics setting has recently emerged as a potential contender due to the experimental availability of massively scalable entangled states.

After connecting continuous-variable and qubit-based quantum computing, this dissertation introduces several novel proposals to engineer specific non-Gaussian quantum resources using projective measurement. These resources include Schrödinger cat, Gottesman-Kitaev-Preskill, binomial code, and coherent photon-subtracted states that would be used to achieve quantum advantages in quantum sensing and quantum computing. Each protocol is designed with current technologies in mind, and a full computational model with realistic imperfections is included to assess the experimental feasibility.

The second part of this dissertation transitions to experimental implementations with a specific focus on the transition-edge sensor, which is a highly quantum efficient photon-number-resolving detector. I detail new methods of processing the output signal and demonstrate the ability to improve resolving capabilities to up to 30 photons per detection channel. This has important implications for quantum information applications, including quantum random number generation and realization of the state engineering protocols discussed in the first portion of the dissertation. Additionally, I present variations on recently developed methods to perform full quantum state tomography that would lead to a quadratic reduction in the number of required measurement settings to completely characterize an unknown state.

Finally, I discuss experimental progress on the generation and characterization of exotic states using the protocol of photon catalysis. This process utilizes a single-photon resource and projection with photon-number-resolving detection to engineer quantum states with non-Gaussian Wigner functions. Current results indicate that this is a viable method to generate exotic states if stability and control of experimental conditions can be improved.