Photon statistics plays a governing role in multiphoton interference. While interference visibility in the standard two-photon case, known as Hong-Ou-Mandel interference, monotonically degrades with higher intensity correlation functions, we show that this monotonicity does not hold for three-photon interference in symmetric circuits. We reveal that, in the discrete Fourier transform circuit, engineered super-Poissonian photon-number fluctuations, realized using a modulated laser, can yield a visibility whose magnitude surpasses that of the single-photon signature. In addition, by tuning the symmetric circuit parameters, we demonstrate that the visibility hierarchy inverts relative to the benchmark of Poissonian statistics. This trade-off implies that quantum and classical advantages are mutually exclusive resources for interference, indicating a form of statistical complementarity.

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• Photon statistics
• Quantum correlations in quantum information
• Quantum optics
• Quantum-to-classical transition