Algorithmical analysis of information-theoretic aspects of secure communication over optical-fiber quantum channels

Abstract

The information-theoretic security of optical-fiber based quantum communication is the fundamental question of quantum cryptography. Quantum cryptographic schemes use photons as information carriers. The physical properties of photons make it possible to use quantum bits to realize unconditionally secure quantum communication over the current standard optical fiber network. Quantum cryptography is one of the most important and advanced fields in the area of quantum information processing. This paper analyzes the information-theoretic security of the most important and prevalent optical-fiber based QKD schemes, such as BB84, Six-state and DPS QKD schemes, using efficient information geometric approaches. We study the information-theoretic impacts of the most general eavesdropping attacks against these protocols using efficient algorithms. Currently, the ability to perform these attacks is well beyond today’s technological capabilities; however, in the future, these types of attacks can be used to eavesdrop on quantum communications over optical fibers. The information-theoretic security of these protocols is analyzed by information geometric algorithms and abstract geometrical objects. To describe the security of the protocols, we introduce the quantum informational ball representation, and we discover the connection between the length of the optical fiber and the radius of the quantum informational ball. For practical reasons, we will also demonstrate our algorithm for the DPS QKD protocol.