  Complementarity, that is the ability of a quantum object to behave either as
a particle or as a wave, is one of the most intriguing features of quantum
mechanics. An exemplary Gedanken experiment, emphasizing such a
measurement-dependent nature, was suggested by Wheeler using single photons.
The subtleness of the idea lies in the fact that the output beam-splitter of a
Mach-Zehnder interferometer is put in or removed after a photon has already
entered the interferometer, thus performing a delayed test of the wave-particle
complementary behavior. Recently, it was proposed that using a quantum analogue
of the output beam-splitter would permit carrying out this type of test after
the detection of the photon and observing wave-particle superposition. In this
paper we describe an experimental demonstration of these predictions using
another extraordinary property of quantum systems, entanglement. We use a pair
of polarization entangled photons composed of one photon whose nature (wave or
particle) is tested, and of a corroborative photon that allows determining
which one, or both, of these two aspects is being tested. This corroborative
photon infers the presence or absence of the beam-splitter and until it is
measured, the beam-splitter is in a superposition of these two states, making
it a quantum beam-splitter. When the quantum beam-splitter is in the state
present or absent, the interferometer reveals the wave or particle nature of
the test photon, respectively. Furthermore, by manipulating the corroborative
photon, we can continuously morph, via entanglement, the test photon from wave
to particle behavior even after it was detected. This result underlines the
fact that a simple vision of light as a classical wave or a particle is
inadequate.
