  Bohr's complementarity principle is of fundamental historic and conceptual
importance for Quantum Mechanics (QM), and states that, with a given
experimental apparatus configuration, one can observe either the wave-like or
the particle-like character of a quantum system, but not both. However, it was
eventually realized that these dual behaviors can both manifest partially in
the same experimental setup, and, using ad hoc proposed measures for the wave
and particle aspects of the quanton, complementarity relations were proposed
limiting how strong these manifestations can be. Recently, a formalism was
developed and quantifiers for the particleness and waveness of a quantum system
were derived from the mathematical structure of QM entailed in the density
matrix's basic properties ($\rho\ge 0$, $\mathrm{Tr}\rho=1$). In this article,
using IBM Quantum Experience quantum computers, we perform experimental tests
of these complementarity relations applied to a particular class of one-qubit
quantum states and also for random quantum states of one, two, and three
qubits.
