We introduce two modal natural deduction systems that are suitable to represent and reason about transforma- tions of quantum registers in an abstract, qualitative, way. Quantum registers represent quantum systems, and can be viewed as the structure of quantum data for quantum oper- ations. Our systems provide a modal framework for reason- ing about operations on quantum registers (unitary trans- formations and measurements) in terms of possible worlds (as abstractions of quantum registers) and accessibility re- lations between these worlds. We give a Kripke–style se- mantics that formally describes quantum register transfor- mations, and prove the soundness and completeness of our systems with respect to this semantics.

A Qualitative Modal Representation of Quantum Register Transformations

MASINI, Andrea;VIGANO', Luca;ZORZI, Margherita
2008

Abstract

We introduce two modal natural deduction systems that are suitable to represent and reason about transforma- tions of quantum registers in an abstract, qualitative, way. Quantum registers represent quantum systems, and can be viewed as the structure of quantum data for quantum oper- ations. Our systems provide a modal framework for reason- ing about operations on quantum registers (unitary trans- formations and measurements) in terms of possible worlds (as abstractions of quantum registers) and accessibility re- lations between these worlds. We give a Kripke–style se- mantics that formally describes quantum register transfor- mations, and prove the soundness and completeness of our systems with respect to this semantics.
9780769531557
Quantum computing; proof theory; modal logic
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11562/316976
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