We construct quantum algorithms to compute the solution and/or physical observables of
nonlinear ordinary differential equations (ODEs) and nonlinear Hamilton-Jacobi equations …

Entanglement purification is used to distill high quality entangled states from several noisy
low quality entangled states, and it plays a key role in quantum repeater. The measurement …

We investigate time complexities of finite difference methods for solving the high-
dimensional linear heat equation, the high-dimensional linear hyperbolic equation and the …

Verifiable blind quantum computation provides a cloud scenario for scalable quantum
information processing. However, constructing one resource-efficient verification protocol is …

Continuous-variable quantum information, encoded into infinite-dimensional quantum
systems, is a promising platform for the realization of many quantum information protocols …

Verifying quantum states is central to certifying the correct operation of various quantum
information processing tasks. In particular, in measurement-based quantum computing …

In this work we develop new methods for the characterisation of continuous variable
quantum states using heterodyne measurement in both the trusted and untrusted settings …

Logic W state, which replaces each physical qubit in a W state with a Greenberger–Horne–
Zeilinger state is robust against photon transmission loss in long‐distance quantum …

Continuous-variable quantum states are of particular importance in various quantum
information processing tasks including quantum communication and quantum sensing …

This thesis focuses on three main questions in the continuous variable and optical settings:
where does a quantum advantage, that is, the ability of quantum machines to outperform …