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Generalised quantum weakest preconditions. (English) Zbl 1197.81047

Summary: A generalisation of the quantum weakest precondition result of D’Hondt and Panangaden is presented. In particular, the most general notion of quantum predicate as positive operator valued measure (termed POVM) is introduced. The previously known quantum weakest precondition result is extended to cover the case of POVM playing the role of a quantum predicate. Additionally, our result is valid in the infinite dimension case and also holds for a quantum program defined as a positive but not necessary completely positive transformation of a quantum states.

MSC:

81P10 Logical foundations of quantum mechanics; quantum logic (quantum-theoretic aspects)
81P15 Quantum measurement theory, state operations, state preparations
28B05 Vector-valued set functions, measures and integrals
46G10 Vector-valued measures and integration

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References:

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