  The possibility of a quantum system to exhibit properties that are akin to
both the classically held notions of being a particle and a wave, is one of the
most intriguing aspects of the quantum description of nature. These aspects
have been instrumental in understanding paradigmatic natural phenomena as well
as to provide nonclassical applications. A conceptual foundation for the wave
nature of a quantum state has recently been presented, through the notion of
quantum coherence. We introduce here a parallel notion for the particle nature
of a quantum state of an arbitrary physical system. We provide elements of a
resource theory of particleness, and give a quantification of the same.
Finally, we provide evidence for a complementarity between the particleness
thus introduced, and the coherence of an arbitrary quantum state.
