Quantum computational logics and Fock space semantics

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 a is identified with a quantum information quantity, represented by a density operator of a Hilbert space, whose dimension depends on the logical complexity of a. At the same time, the logical connectives of the language are interpreted as operations defined in terms of quantum logical gates. Standard quantum computational models can be described as special cases of Fock space models, where the meaning of any sentence is localized in a precise sector of a Fock space F. From an intuitive point of view, the increasing number of particles described in the different sectors of F can be interpreted as increasing information.