  The celebrated Hong-Ou-Mandel effect is the paradigm of two-particle quantum
interference. It has its roots in the symmetry of identical quantum particles,
as dictated by the Pauli principle. Two identical bosons impinging on a beam
splitter (of transmittance 1/2) cannot be detected in coincidence at both
output ports, as confirmed in numerous experiments with light or even matter.
Here, we establish that partial time reversal transforms the beamsplitter
linear coupling into amplification. We infer from this duality the existence of
an unsuspected two-boson interferometric effect in a quantum amplifier (of gain
2) and identify the underlying mechanism as timelike indistinguishability. This
fundamental mechanism is generic to any bosonic Bogoliubov transformation, so
we anticipate wide implications in quantum physics.
