On Coinduction and Quantum Lambda Calculi

Yuxin Deng 1 Yuan Feng 2 Ugo Dal Lago 3, 4
3 FOCUS - Foundations of Component-based Ubiquitous Systems
CRISAM - Inria Sophia Antipolis - Méditerranée , DISI - Dipartimento di Informatica - Scienza e Ingegneria [Bologna]
Abstract : In the ubiquitous presence of linear resources in quantum computation, program equivalence in linear contexts, where programs are used or executed once, is more important than in the classical setting. We introduce a linear contextual equivalence and two notions of bisimilarity, a state-based and a distribution-based, as proof techniques for reasoning about higher-order quantum programs. Both notions of bisimilarity are sound with respect to the linear contextual equivalence, but only the distribution-based one turns out to be complete. The completeness proof relies on a characterisation of the bisimilarity as a testing equivalence.
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Submitted on : Thursday, December 3, 2015 - 10:15:39 AM
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Yuxin Deng, Yuan Feng, Ugo Dal Lago. On Coinduction and Quantum Lambda Calculi. Proceedings of CONCUR 2015, 2015, Madrid, Spain. ⟨10.4230/LIPIcs.CONCUR.2015.427⟩. ⟨hal-01231782⟩

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