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Towards Quantum Multiparty Session Types

Ivan Lanese, Ugo Dal Lago, Vikraman Choudhury

TL;DR

The paper addresses the challenge of formally describing and verifying quantum multiparty protocols by extending Multiparty Session Types with quantum data and operations, yielding Quantum MPSTs (QMPSTs). It develops a calculus with global types and local processes, enforcing linear qubit ownership and providing a concrete operational semantics that combines non-deterministic process interactions with probabilistic quantum measurements. The authors prove key properties—subject reduction, session fidelity, progress, and quantum safety (unique qubit ownership)—and demonstrate the framework on four quantum protocols (Teleportation, Secret Sharing, Bit-Commitment, Key Distribution). This work offers a rigorous, scalable method to specify and verify quantum protocols, with clear guidance for extending MPSTs to broader quantum-era communication tasks and potential links to categorical/denotational semantics.

Abstract

Multiparty Session Types (MPSTs) offer a structured way of specifying communication protocols and guarantee relevant communication properties, such as deadlock-freedom. In this paper, we extend a minimal MPST system with quantum data and operations, enabling the specification of quantum protocols. Quantum MPSTs (QMPSTs) provide a formal notation to describe quantum protocols, both at the abstract level of global types, describing which communications can take place in the system and their dependencies, and at the concrete level of local types and quantum processes, describing the expected behavior of each participant in the protocol. Type-checking relates these two levels formally, ensuring that processes behave as prescribed by the global type. Beyond usual communication properties, QMPSTs also allow us to prove that qubits are owned by a single process at any time, capturing the quantum no-cloning and no-deleting theorems. We use our approach to verify four quantum protocols from the literature, respectively Teleportation, Secret Sharing, Bit-Commitment, and Key Distribution.

Towards Quantum Multiparty Session Types

TL;DR

The paper addresses the challenge of formally describing and verifying quantum multiparty protocols by extending Multiparty Session Types with quantum data and operations, yielding Quantum MPSTs (QMPSTs). It develops a calculus with global types and local processes, enforcing linear qubit ownership and providing a concrete operational semantics that combines non-deterministic process interactions with probabilistic quantum measurements. The authors prove key properties—subject reduction, session fidelity, progress, and quantum safety (unique qubit ownership)—and demonstrate the framework on four quantum protocols (Teleportation, Secret Sharing, Bit-Commitment, Key Distribution). This work offers a rigorous, scalable method to specify and verify quantum protocols, with clear guidance for extending MPSTs to broader quantum-era communication tasks and potential links to categorical/denotational semantics.

Abstract

Multiparty Session Types (MPSTs) offer a structured way of specifying communication protocols and guarantee relevant communication properties, such as deadlock-freedom. In this paper, we extend a minimal MPST system with quantum data and operations, enabling the specification of quantum protocols. Quantum MPSTs (QMPSTs) provide a formal notation to describe quantum protocols, both at the abstract level of global types, describing which communications can take place in the system and their dependencies, and at the concrete level of local types and quantum processes, describing the expected behavior of each participant in the protocol. Type-checking relates these two levels formally, ensuring that processes behave as prescribed by the global type. Beyond usual communication properties, QMPSTs also allow us to prove that qubits are owned by a single process at any time, capturing the quantum no-cloning and no-deleting theorems. We use our approach to verify four quantum protocols from the literature, respectively Teleportation, Secret Sharing, Bit-Commitment, and Key Distribution.
Paper Structure (6 sections, 4 theorems, 15 equations, 13 figures)

This paper contains 6 sections, 4 theorems, 15 equations, 13 figures.

Table of Contents

  1. Introduction
  2. Type system
  3. Semantics
  4. Results
  5. Case Studies
  6. Discussion

Key Result

lemma 1

If a global type ${\color{gtColor} G }\xspace$ is contractive, then the projection ${\color{stColor}{\color{gtColor}{\color{gtColor} G }\xspace}\xspace\! \upharpoonright \!{\boldsymbol{{\color{roleColor}\mathtt{ {\color{roleColor}{\boldsymbol{{\color{roleColor}\mathtt{p}}}}\xspace} }}}}\xspace}$, fo

Figures (13)

  • Figure 1: Syntax of types.
  • Figure 2: Global type transitions
  • Figure 3: Syntax of expressions, processes, and systems
  • Figure 4: Typing rules for expressions, processes, and systems
  • Figure 5: Typing for Alice in Quantum Teleportation
  • ...and 8 more figures

Theorems & Definitions (26)

  • definition 1: Syntax of types
  • definition 2: Global Type Projection
  • definition 3: Global Type Transitions
  • definition 4: Typing contexts
  • definition 5: Typing Judgements
  • definition 6: Typing Rules
  • proof
  • definition 7: Multiparty System Transitions
  • lemma 1
  • proof
  • ...and 16 more