Probabilistic logic of quantum observations

Probabilistic logic of quantum observations

Abstract A probabilistic propositional logic, endowed with a constructor for asserting compatibility of diagonalisable and bounded observables, is presented and illustrated for reasoning about the random results of projective measurements made on a given quantum state. Simultaneous measurements are...

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Veröffentlicht in:Logic journal of the IGPL 2019-05, Vol.27 (3), p.328-370
Hauptverfasser: Sernadas, A, Rasga, J, Sernadas, C, Alcácer, L, Henriques, A B
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container_title Logic journal of the IGPL
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creator Sernadas, A
Rasga, J
Sernadas, C
Alcácer, L
Henriques, A B
description Abstract A probabilistic propositional logic, endowed with a constructor for asserting compatibility of diagonalisable and bounded observables, is presented and illustrated for reasoning about the random results of projective measurements made on a given quantum state. Simultaneous measurements are assumed to imply that the underlying observables are compatible. A sound and weakly complete axiomatisation is provided relying on the decidable first-order theory of real closed ordered fields. The proposed logic is proved to be a conservative extension of classical propositional logic.
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title Probabilistic logic of quantum observations
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