  Projectors are a simple but powerful tool for manipulating and probing
quantum systems. For instance, projecting two-qubit systems onto maximally
entangled states can enable quantum teleportation. While such projectors have
been extensively studied, partially-entangling measurements have been largely
overlooked, especially experimentally, despite their important role in quantum
foundations and quantum information. Here, we propose a way to project two
polarized photons onto any state with a single experimental setup. Our scheme
does not require optical non-linearities or additional photons. Instead, the
entangling operation is provided by Hong-Ou-Mandel interference and
post-selection. The efficiency of the scheme is between 50% and 100%, depending
on the projector. We perform an experimental demonstration and reconstruct the
operator describing our measurement using detector tomography. Finally, we flip
the usual role of measurement and state in Hardy's test by performing a
partially-entangling projector on separable states. The results verify the
entangling nature of our measurement with six standard deviations of
confidence.
