Universal maximally entangled states

Two (\(i=1,2\)) \(d\)-dimensional (d=prime, \(\ne 2\)) particles are accounted for via universal maximally entangled states (MES) bases. The bases are labeled by the particles’ collective (“center of mass” and “relative”) coordinates in a phase space like formalism. Schmidt’s decomposition represents MES via d-terms of single particle product states that form a ‘line’ in a \(d^2\) array of points each designating a single particles product states. Correspondingly, a ‘line’ in a \(d^2\) array of phase space like points designating a \(d^2\) orthonormal MES, represents a two particles product state.