  Maximal entangled states (MES) provide a basis to 2d-dimensional particles
Hilbert space, d=prime $\ne2$. These states allow generalization of the Mean
King Problem. The states may be viewed as build of points each underpins a
product state carrying a mutual unbiased bases (MUB) label or, alternatively,
as product states labeled with center of mass and relative coordinates. The
coordinate-like label of the center of mass and the momentum-like of the
relative coordinates provides a MES account of the Hilbert space in close
analogy with the single particle phase space coordinates.
