Discrimination of geometrically uniform states and the no-signaling principle

The link between quantum state discrimination and the no-signaling principle is applied to discriminating geometrically uniform states. Specifically, the original discrimination problem is converted to constructing the complementary matrix with predetermined off-diagonal entries. Two such constructions are given explicitly, and therefore three upper bounds on the success probability are derived. Those upper bounds are then employed to estimate the robustness of coherence, where we establish a larger class of states with equal robustness of coherence and l (1)-norm of coherence, and provide the exact answer of the robustness of coherence for any states that are diagonalized by Hadamard matrices.