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Boson bunching is not maximized by indistinguishable particles


Boson bunching is among the most remarkable features of quantum physics. A celebrated example in optics is the Hong–Ou–Mandel effect, where the bunching of two photons arises from a destructive quantum interference between the trajectories where they both either cross a beamsplitter or are reflected. This effect takes its roots in the indistinguishability of identical photons. Hence, it is generally admitted—and experimentally verified—that bunching vanishes as soon as photons can be distinguished, for example, when they occupy distinct time bins or have different polarizations. Here we disprove this alleged straightforward link between indistinguishability and bunching by exploiting a recent finding in the theory of matrix permanents. We exhibit a family of optical circuits such that the bunching of photons into two modes can be substantially boosted by making them partially distinguishable via an appropriate polarization pattern. This boosting effect is already visible in a seven-photon interferometric process, making the observation of this phenomenon within reach of current photonic technology. This unexpected behaviour questions our understanding of multiparticle interference in the grey zone between indistinguishable bosons and classical particles.

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Fig. 1: Interferometric set-up.
Fig. 2: Boosted two-mode bunching.
Fig. 3: Photon-number distribution at the output of the circuit achieving boosted two-mode bunching.
Fig. 4: Perturbation effects on boosted two-mode bunching.
Fig. 5: Mechanism at the origin of boosted bunching.
Fig. 6: Bunching violation ratio Rn as a function of n.

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Data availability

The data supporting the study and figures are available upon request. We acknowledge A. Franzen’s ComponentLibrary for use in making the figures.

Code availability

The project relies on the packages PERMANENTS.JL ( and BOSONSAMPLING.JL ( The source code used for generating the figures and the data of this paper is available on GitHub and the data from OSF (


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We thank S. Drury for useful correspondence, as well as F. Flamini and V. Shchesnovich for valuable discussions. B.S. is a Research Fellow and L.N. was a Postdoctoral Researcher of the Fonds de la Recherche Scientifique – FNRS (Belgium). N.J.C. acknowledges support from the Fonds de la Recherche Scientifique – FNRS (Belgium) under grant no. T.0224.18 and by the European Union under project ShoQC within ERA-NET Cofund in Quantum Technologies (QuantERA) programme. L.N. also acknowledges funding from FCT-Fundação para a Ciência e a Tecnologia (Portugal) via project no. CEECINST/00062/2018. This project has also received funding from the European Union’s Horizon 2020 research and innovation programme under Marie Skłodowska-Curie grant agreement no. 956071.

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All authors developed the original concepts, derived the formulae, discussed the results and wrote the paper. B.S. implemented the numerical simulations.

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Correspondence to Nicolas J. Cerf.

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Seron, B., Novo, L. & Cerf, N.J. Boson bunching is not maximized by indistinguishable particles. Nat. Photon. 17, 702–709 (2023).

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