Verifiable Relativistic Quantum Communication

Abstract

Quantum summoning retrieves quantum information prepared at some point in spacetime at another point, which is randomly chosen from a set of points. This thesis presents an efficient quantum summoning protocol based on a quantum error-correcting code, along with encoding and decoding methods. This protocol reduces space complexity as well as gate complexity of encoding compared to previous best results. Our throughout study of quantum summoning paves the way for investigating relativistic quantum cryptography with quantum summoning as a primitive. This thesis also studies a relativistic continuous-variable quantum secret sharing protocol in non-inertial frame, which includes the effect of acceleration of quantum shares in spacetime. By formulating the relativistic effect as a Gaussian lossy channel, we analyze how the fidelity of quantum secret sharing protocol is affected by this relativistic effect. This investigation relaxes the common assumption of secret sharing in inertial frames and this framework can be applied to other relativistic quantum communication protocols. To efficiently verify bosonic quantum channels, I propose a framework of verification of quantum channels plus average-fidelity witness. For both multi-mode Gaussian unitary channels and single-mode amplifying channels, I present efficient verification protocols utilizing only two-mode squeezed vacuum states and homodyne detections. Our work is significant in verification of quantum components in continuous-variable quantum information processing.