The Lattice Dynamics of Completely Entangled States and its Application to Communication Schemes

TL;DR

This paper explores the unique basis of orthogonal entangled states that forms a lattice phase space, enabling enhanced quantum communication schemes through quadratic Hamiltonian dynamics and revealing a pattern linked to number theory.

Contribution

It identifies a unique basis of entangled states forming a lattice phase space and demonstrates how quadratic Hamiltonians can dynamically generate signals for improved communication.

Findings

Enhanced communication schemes using lattice phase space.

Quadratic Hamiltonians induce site-to-site hopping.

Signal phases follow a pattern related to Legendre symbols.

Abstract

(Presented at conference on Fundamental Problems in Physics - UMBC - June 1994) It is shown that among the orthogonal sets of EPR (completely entangled) states there is a unique basis (up to equivalence) that is a also a perfectly resolved set of coherent states with respect to a pair of complementary observables. This basis defines a lattice phase space in which quadratic Hamiltonians constructed from the observables induce site-to-site hopping at discrete time intervals. When recently suggested communication schemes\cite{BENa} are adapted to the lattice they are greatly enhanced, because the finite Heisenberg group structure allows dynamic generation of signal sequences using the quadratic Hamiltonians. We anticipate the possibility of interferometry by determining the relative phases between successive signals produced by the simplest Hamiltonians of this type, and we show that they exhibit a remarkable pattern determined by the number-theoretic Legendre symbol.