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

The quantum beam splitter with many partially indistinguishable photons: multiphotonic interference and asymptotic classical correspondence