  We show that the parity (evenness or oddness) of a nonclassical state of
light has a dominant influence on the interference effects at a balanced beam
splitter, irrespective of the state initially occupying the other input mode.
Specifically, the parity of the nonclassical state gives rise to destructive
interference effects that result in deep valleys in the output joint number
distribution of which the Hong-Ou-Mandel (HOM) effect is a limiting case. The
counter-intuitive influence of even a single photon to control the output of a
beam splitter illuminated by any field, be it a coherent or even a noisy
thermal field, demonstrates the extraordinary power of non-classicality. The
canonical example of total destructive interference of quantum amplitudes
leading to the absence of coincidence counts from a 50/50 beam splitter is the
celebrated HOM effect, characterized by the vanishing of the joint probability
of detecting singe photons in each of the output beams. We show that this is a
limiting case of more general input states upon which a 50/50 BS can create
total, or near total, destructive interference of quantum amplitudes. For odd
photon number input Fock states of arbitrary value n>0 we show that the joint
photon number probabilities vanish when detecting identical photon numbers in
each output beams. We examine the mixing of photon number states of n = 1, 2,
and 3 with a CV state, such as a coherent state of arbitrary amplitude, and a
thermal state. These vanishing joint probabilities form what we call a central
nodal line -- a contiguous set of zeros representing complete destructive
interference of quantum amplitudes. For odd or even photon number Fock states
with n>1 there will be additional off-diagonal pseudo-nodal curves along which
the joint photon number probabilities are either zero, or near zero, which
constitute a near, but not complete, destructive interference.
