  In quantum optics a pure state is considered classical, relative to the
statistics of photodetection, if and only if it is a coherent state. A
different and newer notion of nonclassicality is based on modal entanglement.
One example that relates these two notions is the Hong-Ou-Mandel effect, where
modal entanglement is generated by a beamsplitter from the nonclassical
photon-number state. This suggests that beamsplitters or, more generally,
linear-optical networks are mediators of the two notions of nonclassicality. In
this Brief Report, we show the following: Given a nonclassical
pure-product-state input to an N-port linear-optical network, the output is
almost always mode entangled; the only exception is a product of squeezed
states, all with the same squeezing strength, input to a network that does not
mix the squeezed and anti-squeezed quadratures. Our work thus gives a necessary
and sufficient condition for a linear network to generate modal entanglement
from pure product inputs, a result that is of immediate relevance to the boson
sampling problem.
