  We present the asymptotic analysis of the quantum two-port interferometer in
the $n \rightarrow \infty$ limit of $n$ partially indistinguishable photons.
Using the unitary-unitary duality between port and inner-mode degrees of
freedom, the probability distribution of output port counts can be decomposed
as a sum of contributions from independent channels, each associated to a
spin-$j$ representation of $SU(2)$ and, in this context, to $2 j$ effectively
indistinguishable photons in the channel. Our main result is that the
asymptotic output distribution is dominated by the $O(\sqrt{n})$ channels
around a certain $j^*$ that depends on the degree of indistinguishability. The
asymptotic form is essentially the doubly-humped semi-classical envelope of the
distribution that would arise from $2 j^*$ indistinguishable photons, and which
reproduces the corresponding classical intensity distribution.
