<p>We analyze the detection of quantum coherent states in N-dimensional (ND) modulation formats, in photonic communications applications, where a constellation of quantum states is prepared at the communications transmitter, and a quantum detection strategy is implemented at the receiver to determine as precisely as possible which quantum state was sent. Due to their importance in photonic communications, we analyze symmetric coherent states constellations with constant average photon number per symbol, in 1D (line), 2D (regular polygons), employing modulation on the optical field quadratures; as well as in 3D Platonic regular convex polyhedra and 4D regular polytopes, with modulation on both the field complex amplitude and the polarization degrees of freedom. As a strategy for detection and discrimination of the received multidimensional quantum optical constellation, we employ the quantum square root method (SRM) for the treatment of the quantum photonic communications system performance, arriving at the evaluation of two main performance measures: the mutual information and the error probability for the analyzed constellations.</p>