From quantum computation to quantum logic

Lev D. Beklemishev, Utrecht University

(Joint work with R. Brak)

Abstract: 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.