Digital Quantum Information Processing with Continuous-Variable Systems

The book provides theoretical methods of connecting discrete-variable quantum information processing to continuous-variable one. It covers the two major fields of quantum information processing, quantum communication and quantum computation, leading to achievement of a long-sought full security of quantum key distribution (QKD) and proposal of a resource-efficient method for optical quantum computing.More specifically, the book provides a complete security proof of a continuous-variable QKD protocol under a realistic condition. Security against arbitrary attacks for the continuous-variable QKD under a realistic condition such as finite communication rounds and the use of digitized information processing was a long-standing open problem. In the book, a binary-phase-shift-keying (BPSK)-type continuous-variable QKD protocol is developed, and its finite-size security against general attacks is proved. The key to the proof was a newly developed estimation method for the fidelity to a coherent state using heterodyne measurement and a reduction to the security proof of discrete-variable QKD.The book also provides the unified view for conventionally used approximate Gottesman-Kitaev-Preskill (GKP) codes, which encodes qudits on a continuous-variable system. Although GKP code has many useful quantum information applications such as optical quantum computation and channel coding, the ideal GKP-encoded state is unphysical and the use of its approximated versions is mandatory in practice. On the other hand, the book shows the equivalence of conventionally used approximate GKP codes, which enables direct comparison between researches based on different approximations.The book finally proposes a resource-efficient method to realize the universal optical quantum computation using the GKP code. This can be realized by directly preparing the GKP magic state instead of GKP Pauli states. Feasibility of the proposed protocol is discussed based on the existing experimental proposals for the GKP state preparation.