Natural Quantum Operational Semantics with Predicates

Authors:
Marek Sawerwain;Roman Gielerak
Affiliations:
Institute of Control and Computation Engineering, University of Zielona Góra, ul. Podgórna 50, 65-246 Zielona Góra, Poland;Institute of Control and Computation Engineering, University of Zielona Góra, ul. Podgórna 50, 65-246 Zielona Góra, Poland
Venue:
International Journal of Applied Mathematics and Computer Science - Selected Problems of Computer Science and Control
Year:
2008

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Abstract

A general definition of a quantum predicate and quantum labelled transition systems for finite quantum computation systems is presented. The notion of a quantum predicate as a positive operator-valued measure is developed. The main results of this paper are a theorem about the existence of generalised predicates for quantum programs defined as completely positive maps and a theorem about the existence of a GSOS format for quantum labelled transition systems. The first theorem is a slight generalisation of D'Hondt and Panagaden's theorem about the quantum weakest precondition in terms of discrete support positive operator-valued measures.