  Coherent optical states consist of a quantum superposition of different
photon number (Fock) states, but because they do not form an orthogonal basis,
no photon number states can be obtained from it by linear optics. Here we
demonstrate the reverse, by manipulating a random continuous single-photon
stream using quantum interference in an optical Sagnac loop, we create
engineered quantum states of light with tunable photon statistics, including
approximate weak coherent states. We demonstrate this experimentally using a
true single-photon stream produced by a semiconductor quantum dot in an optical
microcavity, and show that we can obtain light with $g^{(2)}(0)\rightarrow1$ in
agreement with our theory, which can only be explained by quantum interference
of at least 3 photons. The produced artificial light states are, however, much
more complex than coherent states, containing quantum entanglement of photons,
making them a resource for multi-photon entanglement.
