Fibred Coalgebraic Logic and Quantum Protocols

Daniel Marsden
(Department of Computer Science, University of Oxford, UK)

Motivated by applications in modelling quantum systems using coalgebraic techniques, we introduce a fibred coalgebraic logic. Our approach extends the conventional predicate lifting semantics with additional modalities relating conditions on different fibres. As this fibred setting will typically involve multiple signature functors, the logic incorporates a calculus of modalities enabling the construction of new modalities using various composition operations. We extend the semantics of coalgebraic logic to this setting, and prove that this extension respects behavioural equivalence.

We show how properties of the semantics of modalities are preserved under composition operations, and then apply the calculational aspect of our logic to produce an expressive set of modalities for reasoning about quantum systems, building these modalities up from simpler components. We then demonstrate how these modalities can describe some standard quantum protocols. The novel features of our logic are shown to allow for a uniform description of unitary evolution, and support local reasoning such as "Alice's qubit satisfies condition" as is common when discussing quantum protocols.

In Bob Coecke and Matty Hoban: Proceedings of the 10th International Workshop on Quantum Physics and Logic (QPL 2013), Castelldefels (Barcelona), Spain, 17th to 19th July 2013, Electronic Proceedings in Theoretical Computer Science 171, pp. 90–99.
Published: 27th December 2014.

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