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.
@article{arxiv.quant-ph/0201013,
title = {An unsharp logic from quantum computation},
author = {G. Cattaneo and M. L. Dalla Chiara and R. Giuntini and R. Leporini},
journal= {arXiv preprint arXiv:quant-ph/0201013},
year = {2007}
}