Huge Quantum Broadcast Channels and Cryptographic Applications for Separable States

Abstract

Quantum information-theoretic models of secret source-sharing are developed using a general LOCC scheme, i.e. a protocol involving only local operations and classical communication. This is in order to generate a common random key from a shared quantum state at two terminals without allowing an eavesdropper to obtain information about this key. Coding theorems for special separable states are obtained, and bounds to secret key capacity are also derived for more general quantum source states and other models later. In order to prove results for secret source-sharing schemes with a quantum source state also shared with a wiretapper, multi-user systems are studied and the capacity region for the degraded quantum broadcast channel is started to be determined. Using the results of the foregoing chapters, a sufficient bound on the error rate for unconditional security of the BB84 quantum key distribution protocol is proved.