Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1707.09137 · Physical Review A

Bunching effect and quantum statistics of partially indistinguishable photons

Fang‐Wen Sun, Ao Shen, Yang Dong, Xiang-Dong Chen, Guang‐Can Guo

Published Aug 9, 2017• 4 citations
arXivHTMLPDF

Abstract

The quantum statistics of particles is determined by both the spins and the indistinguishability of quantum states. Here we study the quantum statistics of partially distinguishable photons by defining the multiphoton indistinguishability. The photon-bunching coefficient is formulated based on the properties of permutation symmetry and a modified Bose-Einstein statistics is presented with an indistinguishability-induced photon-bunching effect. Moreover, the statistical transition of the photon state is studied for partially distinguishable photons and the results show that the indistinguishability exhibits the same role as that observed in the generation of laser. The results will fill the gap between Bose-Einstein and Poisson statistics for photons and a formula is presented for the study of multiphoton quantum information processes.

DOI
10.1103/physreva.96.023823

Related papers

Indistinguishability-induced classical-to-nonclassical transition of photon statistics

Ao Shen, Bo Du, Ze-Hao Wang +4 more

Photon statistics is one of the key properties of the photon state for the study of quantum coherence and quantum information techniques. Here, we discuss the photon indistinguishability induced bunching effect which can significantly change photon statistics. Through the measurement of the second-order degree of coherence of a mixed photon state composed of a single-photon state and a weak coherent state, the statistical transition from a classical behavior to a nonclassical behavior is experimentally demonstrated by modifying the indistinguishability of the two-photon states. The study will help us to understand and control the photon statistics with a method for quantum optical coherence and quantum information applications. It also indicates that the photon indistinguishability is a key parameter for multipartite quantum coherence.

arXiv:1707.09134•Physical Review A•May 19, 2017•3 citations

A unified framework for anomalous boson bunching

Léo Pioge, Leonardo Novo, Nicolas J. Cerf

Anomalous bunching is a paradoxical quantum interferometric phenomenon in which partially distinguishable photons exhibit a higher probability of bunching into two or more modes than fully indistinguishable photons [Nat. Photonics 17, 702 (2023)]. While this effect is directly linked to violations of certain conjectures on matrix permanents, the mechanism underlying the anomaly is not yet fully understood. Here, we show that boson bunching is governed not by internal indistinguishability alone, but by the total indistinguishability of the postselected output state. Total indistinguishability combines the internal degrees of freedom, such as polarization or arrival time, with the spatial degrees of freedom of their wave functions restricted to the measured output modes of the interferometer. This reformulation preserves the expected connection between boson bunching and total indistinguishability, while clarifying how anomalous bunching can arise. It also reveals several additional facets of the same phenomenon, which are captured within a unified framework. In particular, we exhibit situations in which adding an independent source of distinguishability, either internal or spatial, can enhance multimode or even single-mode bunching probabilities, offering new insights into the subtle role of distinguishability in multiphoton interference.

quant-pharXiv:2607.19499•Jul 23, 2026•0 citations

Anomalous bunching of nearly indistinguishable bosons

Léo Pioge, Benoît Seron, Leonardo Novo +1 more

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.

arXiv:2308.12226•Aug 23, 2023•1 citation

Investigation of the role of indistinguishability in photon bunching and stimulated emission

Bi‐Heng Liu, Fang‐Wen Sun, Yan-Xiao Gong +3 more

Photon bunching effect and stimulated emission of single photons is investigated and observed in the parametric amplification process. It is found that the two-photon interference is responsible for the photon bunching effect and stimulated emission, which is discussed in the temporal degree of freedom and in the presence of photon losses. Moreover, the direct measurement of the indistinguishability of two signal photons without any filtering is accomplished via the correlation between the two idler photons from two cascaded parametric down-conversion processes. This result shows that photon indistinguishability plays an essential role in stimulated emission.

Physical Review A•May 26, 2009•10 citations

A generating-function approach to the interference of squeezed states with partial distinguishability

Matheus Eiji Ohno Bezerra, Valery Shchesnovich

Photon distinguishability is a fundamental property manifested in multiphoton interference and one of the main sources of noise in any photonic quantum information processing. In this work, rather than relying on first-quantization methods, we build on a generating-function framework based on the phase-space formalism to characterize the effects of partial distinguishability on the interference of single-mode squeezed states. Our approach goes beyond commonly used models that represent distinguishability via additional noninterfering modes and captures genuine multiphoton interference effects induced by the overlap of the internal state of the photons. This description provides a clear physical account of how distinguishability gives rise to effective noise in Gaussian boson sampling protocols while enabling a systematic investigation of phase effects arising from the overlap of the internal states.

quant-pharXiv:2602.00071•Jan 21, 2026•0 citations

Observation of a generalized bunching effect of six photons

Xiao-Ling Niu, Yan-Xiao Gong, Bi‐Heng Liu +3 more

When photons are indistinguishably in the same temporal mode, their detection probability is greatly enhanced due to constructive multiphoton interference, as compared to the case when they are distinguishable. We observed for what is believed to be the first time such a photon bunching effect for six photons. The observed enhancement factor in six-photon coincidence measurement is 17+/-2, which is close to a factor of 20 for an ideal case. Our result confirms that the six photons that we obtain have a high degree of indistinguishability.

Optics Letters•Apr 15, 2009•24 citations
The quantum statistics of particles is determined by both the spins and the indistinguishability of quantum states. Here we study the quantum statistics of partially distinguishable photons by defining the multiphoton indistinguishability. The photon-bunching coefficient is formulated based on the properties of permutation symmetry and a modified Bose-Einstein statistics is presented with an indistinguishability-induced photon-bunching effect. Moreover, the statistical transition of the photon state is studied for partially distinguishable photons and the results show that the indistinguishability exhibits the same role as that observed in the generation of laser. The results will fill the gap between Bose-Einstein and Poisson statistics for photons and a formula is presented for the study of multiphoton quantum information processes.
Photon statistics is one of the key properties of the photon state for the study of quantum coherence and quantum information techniques. Here, we discuss the photon indistinguishability induced bunching effect which can significantly change photon statistics. Through the measurement of the second-order degree of coherence of a mixed photon state composed of a single-photon state and a weak coherent state, the statistical transition from a classical behavior to a nonclassical behavior is experimentally demonstrated by modifying the indistinguishability of the two-photon states. The study will help us to understand and control the photon statistics with a method for quantum optical coherence and quantum information applications. It also indicates that the photon indistinguishability is a key parameter for multipartite quantum coherence.
Anomalous bunching is a paradoxical quantum interferometric phenomenon in which partially distinguishable photons exhibit a higher probability of bunching into two or more modes than fully indistinguishable photons [Nat. Photonics 17, 702 (2023)]. While this effect is directly linked to violations of certain conjectures on matrix permanents, the mechanism underlying the anomaly is not yet fully understood. Here, we show that boson bunching is governed not by internal indistinguishability alone, but by the total indistinguishability of the postselected output state. Total indistinguishability combines the internal degrees of freedom, such as polarization or arrival time, with the spatial degrees of freedom of their wave functions restricted to the measured output modes of the interferometer. This reformulation preserves the expected connection between boson bunching and total indistinguishability, while clarifying how anomalous bunching can arise. It also reveals several additional facets of the same phenomenon, which are captured within a unified framework. In particular, we exhibit situations in which adding an independent source of distinguishability, either internal or spatial, can enhance multimode or even single-mode bunching probabilities, offering new insights into the subtle role of distinguishability in multiphoton interference.
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.
Photon bunching effect and stimulated emission of single photons is investigated and observed in the parametric amplification process. It is found that the two-photon interference is responsible for the photon bunching effect and stimulated emission, which is discussed in the temporal degree of freedom and in the presence of photon losses. Moreover, the direct measurement of the indistinguishability of two signal photons without any filtering is accomplished via the correlation between the two idler photons from two cascaded parametric down-conversion processes. This result shows that photon indistinguishability plays an essential role in stimulated emission.
Photon distinguishability is a fundamental property manifested in multiphoton interference and one of the main sources of noise in any photonic quantum information processing. In this work, rather than relying on first-quantization methods, we build on a generating-function framework based on the phase-space formalism to characterize the effects of partial distinguishability on the interference of single-mode squeezed states. Our approach goes beyond commonly used models that represent distinguishability via additional noninterfering modes and captures genuine multiphoton interference effects induced by the overlap of the internal state of the photons. This description provides a clear physical account of how distinguishability gives rise to effective noise in Gaussian boson sampling protocols while enabling a systematic investigation of phase effects arising from the overlap of the internal states.
When photons are indistinguishably in the same temporal mode, their detection probability is greatly enhanced due to constructive multiphoton interference, as compared to the case when they are distinguishable. We observed for what is believed to be the first time such a photon bunching effect for six photons. The observed enhancement factor in six-photon coincidence measurement is 17+/-2, which is close to a factor of 20 for an ideal case. Our result confirms that the six photons that we obtain have a high degree of indistinguishability.