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DOI: 10.4230/LIPIcs.CONCUR.2024.16

Effect Semantics for Quantum Process Calculi

Authors: Lorenzo Ceragioli, Fabio Gadducci, Giuseppe Lomurno, and Gabriele Tedeschi

Published in: LIPIcs, Volume 311, 35th International Conference on Concurrency Theory (CONCUR 2024)

Abstract

The development of quantum communication protocols sparked the interest in quantum extensions of process calculi and behavioural equivalences, but defining a bisimilarity that matches the observational properties of a quantum-capable system is a surprisingly difficult task. The two proposals explicitly addressing this issue, qCCS and lqCCS, do not define an algorithmic verification scheme: the bisimilarity of two processes is proven by comparing their behaviour under all input states. We introduce a new semantic model based on effects, i.e. probabilistic predicates on quantum states that represent their observable properties. We define and investigate the properties of effect distributions and effect labelled transition systems (eLTSs), generalizing probability distributions and probabilistic labelled transition systems (pLTSs), respectively. As a proof of concept, we provide an eLTS-based semantics for a minimal quantum process algebra, which we prove sound and complete with respect to the observable probabilistic behaviour of quantum processes. To the best of our knowledge, ours is the first algorithmically verifiable proposal that abides to the properties of quantum theory.

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Lorenzo Ceragioli, Fabio Gadducci, Giuseppe Lomurno, and Gabriele Tedeschi. Effect Semantics for Quantum Process Calculi. In 35th International Conference on Concurrency Theory (CONCUR 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 311, pp. 16:1-16:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{ceragioli_et_al:LIPIcs.CONCUR.2024.16,
  author =	{Ceragioli, Lorenzo and Gadducci, Fabio and Lomurno, Giuseppe and Tedeschi, Gabriele},
  title =	{{Effect Semantics for Quantum Process Calculi}},
  booktitle =	{35th International Conference on Concurrency Theory (CONCUR 2024)},
  pages =	{16:1--16:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-339-3},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{311},
  editor =	{Majumdar, Rupak and Silva, Alexandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2024.16},
  URN =		{urn:nbn:de:0030-drops-207886},
  doi =		{10.4230/LIPIcs.CONCUR.2024.16},
  annote =	{Keywords: Quantum process calculi, probabilistic LTSs, effect LTSs}
}

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Effect Semantics for Quantum Process Calculi

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