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An unsharp logic from quantum computation

G. Cattaneo·M. L. Dalla Chiara·R. Giuntini·R. Leporini
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Abstract

Logical gates studied in quantum computation suggest a natural logical abstraction that gives rise to a new form of unsharp quantum logic. We study the logical connectives corresponding to the following gates: the Toffoli gate, the NOT and the squareroot of NOT (which admit of natural physical models). This leads to a semantic characterization of a logic that we call computational quantum logic CQL.

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G. Cattaneo, M. L. Dalla Chiara, R. Giuntini, R. Leporini. 2002-01-08. An unsharp logic from quantum computation. https://arxiv.org/abs/quant-ph/0201013

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