  Non-classical states of light are of fundamental importance for emerging
quantum technologies. All optics experiments producing multi-qubit entangled
states have until now relied on outcome post-selection, a procedure where only
the measurement results corresponding to the desired state are considered. This
method severely limits the usefulness of the resulting entangled states. Here,
we show the direct production of polarization-entangled photon triplets by
cascading two entangled downconversion processes. Detecting the triplets with
high efficiency superconducting nanowire single-photon detectors allows us to
fully characterize them through quantum state tomography. We use our
three-photon entangled state to demonstrate the ability to herald Bell states,
a task which was not possible with previous three-photon states, and test local
realism by violating the Mermin and Svetlichny inequalities. These results
represent a significant breakthrough for entangled multi-photon state
production by eliminating the constraints of outcome post-selection, providing
a novel resource for optical quantum information processing.
