  Wave-particle duality epitomizes the counterintuitive character of quantum
physics. A striking illustration is the quantum delay-choice experiment, which
is based on Wheeler's classic delayed-choice gedanken experiment, but with the
addition of a quantum-controlled device enabling wave-to-particle transitions.
Here we realize a quantum delayed-choice experiment in which we control the
wave and the particle states of photons and in particular the phase between
them, thus directly establishing the created quantum nature of the
wave-particle. We generate three-photon entangled states and inject one photon
into a Mach--Zehnder interferometer embedded in a 187-m-long two-photon
Hong-Ou-Mandel interferometer. The third photon is sent 141m away from the
interferometers and remotely prepares a two-photon quantum gate according to
independent active choices under Einstein locality conditions. We have realized
transitions between wave and particle states in both classical and quantum
scenarios, and therefore tests of the complementarity principle that go
fundamentally beyond earlier implementations.
