Abstract

Quantum computing and quantum communication are exciting areas of research at the intersection of physics and computer science, which have great potential for influencing the future development of information processing systems. Quantum cryptography, in particular, is well developed. Commercial Quantum Key Distribution systems are easily available and several QKD networks have been built in various parts of the world. However, the security of the protocols rely on information-theoretic proofs, which may or may not reflect actual system behaviour, and testing of the implementations. We present a novel framework for modelling and proving quantum protocols using the proof assistant Coq. We provide a Coq library for quantum bits (qubits), quantum gates, and quantum measurement. We implement and prove a simple quantum coin flipping protocol. As a step towards verifying practical quantum communication and security protocols, such as Quantum Key Distribution, we support multiple qubits, communication and entanglement. We further illustrate these concepts by modelling the Quantum Teleportation Protocol, which communicates the state of an unknown quantum bit using only a classical channel.