Verification of Quantum Protocols Adopting Physically Admissible Schedulers

2026-04-26

AI Summary

This work addresses a critical limitation in existing methods for verifying quantum protocols, which erroneously distinguish physically equivalent processes due to the introduction of probabilistic nondeterminism inconsistent with physical observations. To resolve this, the paper proposes lqCCS, a quantum concurrent process calculus that eliminates unphysical nondeterminism while preserving the expressiveness required to model real-world protocols. This is achieved through a semantics based on quantum generalized probability distributions, constraints imposed by physically admissible schedulers—a novel integration into quantum process calculi—and a saturation-based labeled bisimulation. The framework establishes behavioral equivalence as a congruence with respect to parallel composition and proves the adequacy of the bisimulation under mixtures of indistinguishable quantum states. It enables compositional reasoning and successfully supports equivalence checking for a broad class of processes and formal verification of multiple realistic quantum protocols.

Technology Category

• Machine Learning: Quantum Machine Learning
• Knowledge Representation and Reasoning: Qualitative Reasoning
• Reasoning under Uncertainty: Uncertainty Representations

Application Category

• Security and Privacy: Large-scale security measurements
• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

Reliable verification techniques for quantum communication protocols are of paramount importance, given their high implementation cost and critical contexts of application. Extensions of process calculi have been proposed, together with various notions of behavioural equivalence. However, their standard probabilistic models turn out to introduce some non-deterministic capabilities not aligned with the observational properties of physical quantum systems, leading to bisimilarity notions that distinguish physically equivalent processes. Nonetheless, non-deterministic features are fundamental to account for inputs, environments and adversarial behaviour. To address this issue, we propose lqCCS, a process calculus that integrates concurrency, non-determinism and quantum capabilities. We introduce a novel semantics in terms of distributions, where explicit physically admissible schedulers constrain probabilistic composition and forbid ill-defined non-deterministic moves, while preserving the expressivity needed to model real-world protocols. We investigate a scheduled version of saturated bisimilarity, pairing two processes if no observer can tell them apart, and we verify its adequacy by lifting a known result from quantum mechanics to lqCCS: equivalent processes acting on indistinguishable mixtures of quantum states are correctly recognized as bisimilar. Finally, we give an alternative semantics and a labelled bisimilarity based on a quantum generalization of probability distributions. This characterizes our behavioural equivalence as a congruence with respect to the parallel operator, enabling compositional reasoning without the need to explicitly check all possible contexts. We describe a rich class of lqCCS processes for which equivalence is decidable using standard techniques, and we analyse real-world quantum communication protocols.

Problem

• quantum protocols
• behavioural equivalence
• non-determinism
• physically admissible schedulers
• process calculi

Innovation

• quantum process calculus
• physically admissible schedulers
• scheduled bisimilarity
• quantum probability distributions
• compositional verification