Computational Logic on Fock Space

Abstract

Fock space may provide an important mathematical model for quantum computation. For this reason, it may be useful to generalize previous work on computational logic to the Fock space framework. The basic construction of this computational logic is the set D(H) of density operators on a Fock space H. We first define n-sector p _n(ρ) and total probabilities p(ρ) of elements ρ ∈ D(H). We next discuss NOT, AND, and OR operations on D(H). Natural equivalence classes and Scotian elements are described. We also discuss minimal and maximal elements and quantum numbers for the equivalence classes. We finally treat the operation $\sqrt {NOT}$ and the stronger equivalence classes associated with this operation.