Quantum computational semantics on fock space

In the Fock space semantics, meanings of sentences are identified with density operators of the (unsymmetrized) Fock space ℱ based on the Hilbert space ℂ2. Generally, the meaning of a sentence is smeared over different sectors of ℱ. The standard quantum computational semantics is a limit case of the Fock space semantics, where the meaning of any sentence α only "lives" in one sector of ℱ, which is determined by the logical complexity of α. We prove that the global Fock space semantics and the standard quantum computational semantics characterize the same logic.