(Joint work with R. Brak)
Quantum computation is based on the notion of quantum circuit.
We discuss the possibility of defining a logic that would relate to
quantum circuits in the same way as classical boolean logic relates to
boolean circuits. We examine this analogy in some detail.
In particular, we consider specific features of quantum information
that the intended logic has to capture emphasising the role
of quantum measurement. We come forward with some proposals
that differ in the extent measurement can be used.
We compare this work with the traditional Birkhoff-von Neumann style quantum
logics as well as with the recent proposals by a
group of Italian logicians (M.L. Dalla Chiara et al. 2002, 2003).
We observe similarilites with yet another
approach by Y. Lafont (2003) based on monoidal categories.
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