Computer Science Logic and 8th Kurt Gödel Colloquium
Ron van der Meyden, Manas Patra: A Logic for Probability in Quantum Systems
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Quantum computation deals with projective measurements and unitary transformations in finite dimensional Hilbert spaces. The paper presents a propositional logic designed to describe quantum computation at an operational level by supporting reasoning about probabilities assosciated to such measurements: measurement probabilities and transition probabilities ( a quantum analogue of conditonal probabilities). We present two axiomatisations, one for the logic as a whole and one for the fragment dealing with measurement probabilities. These axiomatisations are proved to be sound and complete. The logic is shown to be decidable and we provide results characterising its complexity in a number of cases.
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