Abstract
Maximal entangled states provide a basis to two d-dimensional particles in Hilbert space, d = prime ≠ 2. The maximally entangled states forming this basis are uniquely related to product states in the collective, center of mass and relative, coordinates. These states are associated (underpinned) with lines of finite geometry whose constituent points are associated with product states carrying mutual unbiased bases labels. This representation is shown to be convenient for the study of the mean King problem and a variant thereof, termed ‘tracking the King’, which proves to be a novel quantum communication channel. The main topics and notations used are reviewed in an attempt to keep the paper self contained.
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