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A Logic for Probability in Quantum Systems

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Computer Science Logic (CSL 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2803))

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Abstract

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 the probabilities associated to such measurements: measurement probabilities, and transition probabilities (a quantum analogue of conditional probabilities). We present two axiomatizations, one for the logic as a whole and one for the fragment dealing just with measurement probabilities. These axiomatizations are proved to be sound and complete. The logic is also shown to be decidable, and we provide results characterizing its complexity in a number of cases.

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© 2003 Springer-Verlag Berlin Heidelberg

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van der Meyden, R., Patra, M. (2003). A Logic for Probability in Quantum Systems. In: Baaz, M., Makowsky, J.A. (eds) Computer Science Logic. CSL 2003. Lecture Notes in Computer Science, vol 2803. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45220-1_34

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  • DOI: https://doi.org/10.1007/978-3-540-45220-1_34

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40801-7

  • Online ISBN: 978-3-540-45220-1

  • eBook Packages: Springer Book Archive

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