Probabilistic Model--Checking of Quantum Protocols

TL;DR

This paper introduces automated probabilistic model-checking techniques for verifying quantum communication protocols, providing a rigorous, simpler alternative to traditional physics-based analysis, demonstrated on key quantum protocols.

Contribution

The paper presents a novel application of probabilistic model-checking to quantum protocols, enabling formal verification and analysis using existing tools like PRISM.

Findings

Successfully modelled superdense coding, quantum teleportation, and quantum error correction protocols.

Verified correctness properties of these quantum protocols.

Established a foundation for analyzing larger quantum systems such as quantum cryptography.

Abstract

We establish fundamental and general techniques for formal verification of quantum protocols. Quantum protocols are novel communication schemes involving the use of quantum-mechanical phenomena for representation, storage and transmission of data. As opposed to quantum computers, quantum communication systems can and have been implemented using present-day technology; therefore, the ability to model and analyse such systems rigorously is of primary importance. While current analyses of quantum protocols use a traditional mathematical approach and require considerable understanding of the underlying physics, we argue that automated verification techniques provide an elegant alternative. We demonstrate these techniques through the use of PRISM, a probabilistic model-checking tool. Our approach is conceptually simpler than existing proofs, and allows us to disambiguate protocol definitions and assess their properties. It also facilitates detailed analyses of actual implemented systems. We illustrate our techniques by modelling a selection of quantum protocols (namely superdense coding, quantum teleportation, and quantum error correction) and verifying their basic correctness properties. Our results provide a foundation for further work on modelling and analysing larger systems such as those used for quantum cryptography, in which basic protocols are used as components.