Generalised quantum weakest preconditions

Authors:
Roman Gielerak;Marek Sawerwain
Affiliations:
Institute of Control and Computation Engineering, Faculty of Electrical Engineering, Computer Science and Telecommunications, University of Zielona Góra, Zielona Góra, Poland 65-246;Institute of Control and Computation Engineering, Faculty of Electrical Engineering, Computer Science and Telecommunications, University of Zielona Góra, Zielona Góra, Poland 65-246
Venue:
Quantum Information Processing
Year:
2010

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Abstract

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 has been extended to cover the case of POVM playing the role of a quantum predicate. Additionally, our result is valid in infinite dimension case and also holds for a quantum programs defined as a positive but not necessary completely positive transformations of a quantum states.