  Quantum theory has the intriguing feature that is inconsistent with
noncontextual hidden variable models, for which the outcome of a measurement
does not depend on which other compatible measurements are being performed
concurrently. While various proofs of such contextual behavior of quantum
systems have been established, relatively little is known concerning the
possibility to demonstrate this intriguing feature for indistinguishable
particles. Here, we show in a simple and systematic manner that with projective
measurements alone, it is possible to demonstrate quantum contextuality for
such systems of arbitrary Hilbert space dimensions, including those
corresponding to a qubit. Our demonstration is applicable to a single fermion
as well as multiple fermions, and thus also a composite boson formed from an
even number of fermions. In addition, our approach gives a clear demonstration
of the intimate connection between complementarity and contextuality, two
seemingly unrelated aspects of quantum theory.
