Irreversibility in Quantum Computational Logics

In this paper we discuss an approach to quantum computation where the basic information units (qubits and quregisters) are replaced by density operators and the restriction to unitary operators as logical gates is lifted through the introduction of the more general concept of quantum operation ( [17], [1]). This perspective is especially suited to provide a physical description of open systems. In particular, we illustrate the advantages of this approach over the standard one and show that it can account for two important irreversible transformations already considered in the literature: the irreversible conjunction IAND and the fuzzy-like Łukasiewicz disjunction ⊕.