Formalization of quantum protocols using Coq

Conference paper

Boender, J., Kammueller, F. and Nagarajan, R. 2015. Formalization of quantum protocols using Coq. The 12th International Workshop on Quantum Physics and Logic (QPL 2015). Oxford, United Kingdom 15 - 17 Jul 2015 pp. 71-83
TypeConference paper
TitleFormalization of quantum protocols using Coq
AuthorsBoender, J., Kammueller, F. and Nagarajan, R.
Abstract

Quantum Information Processing, which is an exciting area of research at the intersection of physics and computer science, has great potential for influencing the future development of information pro- cessing systems. The building of practical, general purpose Quantum Computers may be some years into the future. However, Quantum Communication and Quantum Cryptography are well developed. Commercial Quantum Key Distribution systems are easily available and several QKD networks have been built in various parts of the world. The security of the protocols used in these implementations rely on information-theoretic proofs, which may or may not reflect actual system behaviour. Moreover, testing of implementations cannot guarantee the absence of bugs and errors. This paper presents a novel framework for modelling and verifying quantum protocols and their implementations using the proof assistant Coq. We provide a Coq library for quantum bits (qubits), quantum gates, and quantum mea- surement. As a step towards verifying practical quantum communication and security protocols such as Quantum Key Distribution, we support multiple qubits, communication and entanglement. We illustrate these concepts by modelling the Quantum Teleportation Protocol, which communicates the state of an unknown quantum bit using only a classical channel.

Research GroupFoundations of Computing group
ConferenceThe 12th International Workshop on Quantum Physics and Logic (QPL 2015)
Page range71-83
ISSN2075-2180
Publication dates
Print04 Nov 2015
Publication process dates
Deposited03 Jun 2015
Accepted01 Jun 2015
Submitted2015
Output statusPublished
Web address (URL)http://dx.doi.org/10.4204/EPTCS.195.6
LanguageEnglish
Book titleEPTCS 195: Proceedings 12th International Workshop on Quantum Physics and Logic
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Preibusch, S. and Kammueller, F. 2008. Checking the TWIN elevator system by translating object-Z to SMV. Lecture Notes in Computer Science. 4916, pp. 38-55. https://doi.org/10.1007/978-3-540-79707-4
Composing safely: a type system for aspects
Kammueller, F. and Sudhof, H. 2008. Composing safely: a type system for aspects. Lecture Notes in Computer Science. 4954, pp. 231-247. https://doi.org/10.1007/978-3-540-78789-1_18
Security analysis of private data enquiries in Erlang
Kammueller, F. and Kammueller, R. 2009. Security analysis of private data enquiries in Erlang. International Journal on Advances in Security. 2 (2&3), pp. 242-255.
An asynchronous distributed component model and its semantics
Henrio, L., Kammueller, F. and Rivera, M. 2009. An asynchronous distributed component model and its semantics. Lecture Notes in Computer Science. 5751, pp. 159-179. https://doi.org/10.1007/978-3-642-04167-9_9
A framework for reasoning on component composition
Henrio, L., Kammueller, F. and Khan, M. 2010. A framework for reasoning on component composition. Lecture Notes in Computer Science. 6286, pp. 1-20. https://doi.org/10.1007/978-3-642-17071-3_1
Formalizing non-interference for a simple bytecode language in Coq
Kammueller, F. 2008. Formalizing non-interference for a simple bytecode language in Coq. Formal Aspects of Computing. 20 (3), pp. 259-275.
Mechanical analysis of finite idempotent relations
Kammueller, F. 2011. Mechanical analysis of finite idempotent relations. Fundamenta Informaticae. 107 (1), pp. 43-65. https://doi.org/10.3233/FI-2011-392
Privacy enforcement and analysis for functional active objects
Kammueller, F. 2011. Privacy enforcement and analysis for functional active objects. Lecture Notes in Computer Science. 6514, pp. 93-107. https://doi.org/10.1007/978-3-642-19348-4_8