Product Łukasiewicz Quantum Logic

Abstract

The theory of logical gates in quantum computation has suggested new forms of quantum logic, called quantum computational logics. The basic semantic idea is the following: the meaning of a sentence is identified with a density operator (called qumix). In this framework, any sentence α of the language gives rise to a quantum circuit that transforms the qumix associated to the atomic subformulas of α into the qumix associated to α. In this paper we enrich the language by adding a new connective which expresses truncated sum.