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Maximal entangled states (MES) provide a basis to two d-dimensional particlesHilbert space, d=prime $\ne 2$. The MES forming this basis are product statesin the collective, center of mass and relative, coordinates. These states areassociated (underpinned) with lines of finite geometry whose constituent pointsare associated with product states carrying Mutual Unbiased Bases (MUB) labels.This representation is shown to be convenient for the study of the Mean KingProblem and a variant thereof, termed Tracking the King which proves to be anovel quantum communication channel. The main topics, notions used are reviewedin an attempt to have the paper self contained.

Maximal Entanglement, Collective Coordinates and Tracking the King