Engineering of quantum systems with variables inGF(pℓ)
Apostol Vourdas · Journal of Physics Conference Series · 2011
A system comprised of l subsystems, each of which is described with variables in p, is considered. Position and momentum states in this l-partite system can be labelled with elements in GF(pl). It is shown that the whole quantum formalism can be expressed in terms of Galois arithmetic, if and only if the Hamiltonian belongs to a particular subset of the set of all Hamiltonians of this l-partite system (we say that these Hamiltonians are compatible with GF(pll)). Several examples of such Hamiltonians are presented.