Remarkable Phase Oscillations Appearing in the Lattice Dynamics of Einstein-Podolsky-Rosen States

Abstract

It is shown that the transformations of Einstein-Podolsky-Rosen states such as those used in communication and cryptography schemes can be described as a hopping motion on a finite phase space lattice associated with a finite Heisenberg group. Quantum mechanical Hamiltonians that generate the hopping are shown to cause phase oscillations characterized by the number-theoretic Legendre symbol.