  The commonly assumed straight link between boson bunching and particle
indistinguishability in quantum interferometry has recently been challenged
[Nat. Photon. 17, 702 (2023)]. Exploiting the connection between quantum
optical interferences and matrix permanents, it appeared that bunching effects
may arise that exceed the expected limit of fully indistinguishable particles
by injecting peculiar polarization states of partially distinguishable photons
in some interferometers. Surprisingly, all states giving rise to such an
anomalous bunching were found to be far from the state of fully
indistinguishable particles, raising the question of whether this intriguing
phenomenon might even possibly exist with nearly indistinguishable particles.
Here, we answer this question positively by relating it to a mathematical
conjecture on matrix permanents dating from 1986, whose physical interpretation
had not yet been unveiled. Using a recently found counterexample to this
conjecture, we demonstrate that there is an optical interferometer involving 8
photons in 10 modes such that the probability that all photons bunch into two
output modes can be enhanced by suitably perturbing the state of all photons
having the same polarization. Such a finding reflects still another -- even
less expected -- facet of anomalous boson bunching.
