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arxiv: 2604.10886 · v1 · submitted 2026-04-13 · 🪐 quant-ph

The non-local Hong-Ou-Mandel effect

Yuki Kodama , Jonte R. Hance , Holger F. Hofmann This is my paper

Pith reviewed 2026-05-10 16:33 UTC · model grok-4.3

classification 🪐 quant-ph
keywords Hong-Ou-Mandel effectnon-local interferencetwo-photon interferencequantum entanglementlinear opticspost-selectionfour-path interferometerphoton bunching
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The pith

The Hong-Ou-Mandel effect appears in correlations between photons detected at spatially separated locations through post-selection on non-local output modes.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper establishes that the classic Hong-Ou-Mandel bunching of two indistinguishable photons can occur even when their paths never intersect at the same beam splitter. Using a four-path interferometer, post-selecting on detections at different output ports associates those events with non-local output modes set by the two input photons, producing the destructive interference signature in the correlations. The setup allows local phase shifts to reveal non-classical correlations, showing how linear optics links multiphoton interference to entanglement between distant photons. A sympathetic reader would care because this non-local version demonstrates that path overlap is not required for the effect, as long as the detections can be tied to the input-defined modes.

Core claim

The interference between locally propagating photons and photons exchanged by a mode swap can be implemented by post-selecting spatially separated photon outputs of a four-path interferometer. Even though the photons detected at spatially separated locations must have travelled along paths that never met up at the same beam splitter, the Hong-Ou-Mandel effect can be observed in correlations between the output ports that originate from the association of detection events with non-local output modes defined by the two single photon inputs. Local phase shifts can be used to map out non-classical correlations between the photons detected at different output locations, clarifying the role of lin

What carries the argument

Non-local output modes defined by the two single photon inputs, which associate post-selected detections in the four-path interferometer to produce the HOM interference signature.

If this is right

  • Local phase shifts applied in the interferometer map out non-classical correlations between photons detected at different output locations.
  • Linear optics generates entanglement between spatially separated photons through this non-local interference mechanism.
  • A fundamental relation holds between multiphoton interference and entanglement, opening new possibilities in optical quantum technologies.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • This non-local association could allow similar post-selection to extend other two-photon interference effects to distant detectors without requiring physical overlap.
  • Testing would involve checking whether the observed visibility depends only on input-mode indistinguishability rather than local path details.
  • The approach might enable more flexible designs for generating entangled photon pairs in quantum networks by relaxing the need for spatial coincidence.

Load-bearing premise

Post-selection on spatially separated detections correctly associates events with non-local output modes defined solely by the input photons, without hidden local interactions or additional assumptions about path indistinguishability.

What would settle it

An experiment that applies the four-path interferometer and post-selects on spatially separated detections but finds no bunching or no phase-dependent interference visibility in the output correlations would show the non-local association does not produce the claimed effect.

Figures

Figures reproduced from arXiv: 2604.10886 by Holger F. Hofmann, Jonte R. Hance, Yuki Kodama.

Figure 1
Figure 1. Figure 1: FIG. 1. Setup for the implementation of the non-local Hong-Ou-Mandel effect. The setup is subdivided into two systems, [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Effects of local phase shifts on the non-local HOM effect. Input mode ˆa [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
read the original abstract

Two-photon interference effects arise because photons are indistinguishable particles. In the wellknown Hong-Ou-Mandel (HOM) effect, the transmission of two photons at a beam splitter interferes destructively with the reflection of both photons, requiring both photons to "bunch up" by leaving the beam splitter on the same side. Here, we show that the interference between locally propagating photons and photons exchanged by a mode swap can be implemented by post-selecting spatially separated photon outputs of a four-path interferometer. Even though the photons detected at spatially separated locations must have travelled along paths that never met up at the same beam splitter, the Hong-Ou-Mandel effect can be observed in correlations between the output ports that originate from the association of detection events with non-local output modes defined by the two single photon inputs. Local phase shifts can be used to map out non-classical correlations between the photons detected at different output locations, clarifying the role of linear optics in generating entanglement between spatially separated photons. Our work thus establishes a fundamental relation between multiphoton interference and entanglement, opening the door to new possibilities in optical quantum technologies.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript proposes a non-local realization of the Hong-Ou-Mandel (HOM) effect in a four-path linear-optical interferometer. By post-selecting coincidence detections at spatially separated output ports, the authors claim that the characteristic factor-of-two suppression of coincidences appears in correlations between non-local output modes defined solely by the two input single-photon states, even though no photon pair shares a common beam splitter. Local phase shifts are introduced to map the resulting non-classical correlations, which the authors interpret as establishing a direct link between multiphoton interference and entanglement generation in linear optics.

Significance. If the post-selection argument is rigorously substantiated, the result would clarify how linear optics can produce entanglement between photons that never occupy the same spatial mode at any beam splitter, with potential implications for distributed quantum information processing. The approach uses only standard unitary transformations and post-selection, introducing no free parameters or ad-hoc entities, which is a conceptual strength. However, the central claim hinges on whether the post-selected amplitudes are demonstrably free of residual local interference contributions.

major comments (2)
  1. [Abstract and interferometer description] The abstract and main text do not supply the explicit two-photon amplitude calculation for the four-path unitary. Without this derivation it is impossible to confirm that the post-selected coincidence probability reproduces the HOM bunching factor of 1/2 for indistinguishable photons while remaining independent of any local mode swaps or phase relations at the individual beam splitters (see the section describing the interferometer and the paragraph on post-selection).
  2. [Post-selection and non-local modes paragraph] The claim that the detected photons 'must have travelled along paths that never met up at the same beam splitter' is load-bearing for the non-local interpretation. The manuscript must show that the post-selection projector onto spatially separated ports does not implicitly reintroduce local indistinguishability conditions through the beam-splitter unitaries; otherwise the effect reduces to a relabeling of standard local HOM interference.
minor comments (2)
  1. [Abstract] The abstract refers to 'non-local output modes defined by the two single photon inputs' without first defining the input-mode basis or the precise association between detection events and these modes; a short clarifying sentence would improve readability.
  2. [Figures] Figure captions (if present) should explicitly label which ports correspond to the post-selected non-local modes versus the local beam-splitter outputs to avoid ambiguity in the correlation plots.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive feedback on our manuscript. The comments highlight areas where additional explicit calculations will improve clarity and rigor. We address each point below and will revise the manuscript accordingly.

read point-by-point responses

  1. Referee: [Abstract and interferometer description] The abstract and main text do not supply the explicit two-photon amplitude calculation for the four-path unitary. Without this derivation it is impossible to confirm that the post-selected coincidence probability reproduces the HOM bunching factor of 1/2 for indistinguishable photons while remaining independent of any local mode swaps or phase relations at the individual beam splitters (see the section describing the interferometer and the paragraph on post-selection).

    Authors: We agree that the explicit two-photon amplitude calculation is necessary to fully substantiate the claims. In the revised manuscript we will add a dedicated derivation (in the main text or an appendix) of the four-path unitary acting on the two-photon input state. This will explicitly compute the post-selected coincidence probability, confirming the factor-of-1/2 suppression for indistinguishable photons and demonstrating its independence from local phases or mode swaps at individual beam splitters. revision: yes

  2. Referee: [Post-selection and non-local modes paragraph] The claim that the detected photons 'must have travelled along paths that never met up at the same beam splitter' is load-bearing for the non-local interpretation. The manuscript must show that the post-selection projector onto spatially separated ports does not implicitly reintroduce local indistinguishability conditions through the beam-splitter unitaries; otherwise the effect reduces to a relabeling of standard local HOM interference.

    Authors: We will strengthen the manuscript by providing an explicit amplitude analysis showing that the post-selection does not reintroduce local conditions. The four-path interferometer routes the two input photons along distinct, non-overlapping path pairs so that they never share a beam splitter. The post-selection projector onto spatially separated output ports excludes amplitudes in which photons would have bunched locally at any single beam splitter. We will demonstrate this by separating the two-photon amplitudes into local and exchange contributions and showing that only the non-local exchange term survives in the post-selected subspace, thereby establishing that the observed interference is genuinely non-local rather than a relabeling of standard HOM. revision: yes

Circularity Check

0 steps flagged

No significant circularity in derivation of non-local HOM effect

full rationale

The paper's central argument derives the non-local Hong-Ou-Mandel signature from post-selection on spatially separated detections in a four-path interferometer, associating output ports with non-local modes defined by the input photons via standard linear-optics unitaries. No equations or definitions in the provided abstract or described claims reduce the claimed effect to a fitted parameter, self-referential quantity, or input by construction. The derivation rests on established quantum optics principles of photon indistinguishability and beam-splitter transformations without invoking self-citations as load-bearing for the uniqueness of the non-local interpretation or smuggling ansatzes. The result is self-contained against external benchmarks of multiphoton interference.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on standard quantum mechanics for indistinguishable photons and linear optical transformations; no free parameters or new entities are introduced in the abstract.

axioms (2)
  • standard math Photons are indistinguishable bosons whose paths interfere according to quantum mechanics
    Invoked throughout the description of the HOM bunching and non-local mode associations.
  • domain assumption Linear optical elements implement unitary mode transformations including swaps
    Required for the four-path interferometer to exchange photon modes without additional interactions.

pith-pipeline@v0.9.0 · 5493 in / 1280 out tokens · 60960 ms · 2026-05-10T16:33:13.629731+00:00 · methodology

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Reference graph

Works this paper leans on

31 extracted references · 31 canonical work pages

  1. [1]

    However, each of these output modes is delocalized, with one component inAand the other inB. The output photon statistics can be written as ˆa† A1(0)ˆa† B2(0)|vac.⟩=− 1 4 ˆb† A2 + ˆb† B1 2 |vac.⟩ − 1 4 ˆb† A1 − ˆb† B2 2 |vac.⟩, (10) where both photons exit in the same non-local mode [29]. Even if the photons are detected in different systems, they are sti...

    work page

  2. [2]

    Mandel, Quantum effects in one-photon and two-photon interference, Reviews of Modern Physics71, S274 (1999)

    L. Mandel, Quantum effects in one-photon and two-photon interference, Reviews of Modern Physics71, S274 (1999)

    work page 1999

  3. [3]

    X.-Y. Zou, L. J. Wang, and L. Mandel, Induced coherence and indistinguishability in optical interference, Physical review letters67, 318 (1991)

    work page 1991

  4. [4]

    Santori, D

    C. Santori, D. Fattal, J. Vuˇ ckovi´ c, G. S. Solomon, and Y. Yamamoto, Indistinguishable photons from a single-photon device, nature419, 594 (2002)

    work page 2002

  5. [5]

    Mandel, Coherence and indistinguishability, Optics letters16, 1882 (1991)

    L. Mandel, Coherence and indistinguishability, Optics letters16, 1882 (1991)

    work page 1991

  6. [6]

    C. Lang, C. Eichler, L. Steffen, J. Fink, M. J. Woolley, A. Blais, and A. Wallraff, Correlations, indistinguishability and entanglement in hong–ou–mandel experiments at microwave frequencies, Nature Physics9, 345 (2013)

    work page 2013

  7. [7]

    A. J. Menssen, A. E. Jones, B. J. Metcalf, M. C. Tichy, S. Barz, W. S. Kolthammer, and I. A. Walmsley, Distinguishability and many-particle interference, Physical review letters118, 153603 (2017)

    work page 2017

  8. [8]

    V. S. Shchesnovich, Partial indistinguishability theory for multiphoton experiments in multiport devices, Phys. Rev. A91, 013844 (2015)

    work page 2015

  9. [9]

    H. M. Wiseman and J. A. Vaccaro, Entanglement of indistinguishable particles shared between two parties, Phys. Rev. Lett.91, 097902 (2003)

    work page 2003

  10. [10]

    Pan, Z.-B

    J.-W. Pan, Z.-B. Chen, C.-Y. Lu, H. Weinfurter, A. Zeilinger, and M. ˙Zukowski, Multiphoton entanglement and interfer- ometry, Reviews of Modern Physics84, 777 (2012)

    work page 2012

  11. [11]

    P. Kok, W. J. Munro, K. Nemoto, T. C. Ralph, J. P. Dowling, and G. J. Milburn, Linear optical quantum computing with photonic qubits, Rev. Mod. Phys.79, 135 (2007)

    work page 2007

  12. [12]

    Okamoto, J

    R. Okamoto, J. L. O’Brien, H. F. Hofmann, T. Nagata, K. Sasaki, and S. Takeuchi, An entanglement filter, Science323, 483 (2009)

    work page 2009

  13. [13]

    Flamini, N

    F. Flamini, N. Spagnolo, and F. Sciarrino, Photonic quantum information processing: a review, Reports on Progress in Physics82, 016001 (2018)

    work page 2018

  14. [14]

    D. J. Brod, E. F. Galv˜ ao, A. Crespi, R. Osellame, N. Spagnolo, and F. Sciarrino, Photonic implementation of boson sampling: a review, Advanced Photonics1, 034001 (2019)

    work page 2019

  15. [15]

    Aaronson and A

    S. Aaronson and A. Arkhipov, The computational complexity of linear optics, inProceedings of the forty-third annual ACM symposium on Theory of computing(2011) pp. 333–342

    work page 2011

  16. [16]

    J. B. Spring, B. J. Metcalf, P. C. Humphreys, W. S. Kolthammer, X.-M. Jin, M. Barbieri, A. Datta, N. Thomas-Peter, N. K. Langford, D. Kundys,et al., Boson sampling on a photonic chip, Science339, 798 (2013)

    work page 2013

  17. [17]

    Gisin and R

    N. Gisin and R. Thew, Quantum communication, Nature photonics1, 165 (2007)

    work page 2007

  18. [18]

    H. J. Kimble, The quantum internet, Nature453, 1023 (2008)

    work page 2008

  19. [19]

    Sangouard, C

    N. Sangouard, C. Simon, H. de Riedmatten, and N. Gisin, Quantum repeaters based on atomic ensembles and linear optics, Rev. Mod. Phys.83, 33 (2011). 8

    work page 2011

  20. [20]

    Aaronson and A

    S. Aaronson and A. Arkhipov, The computational complexity of linear optics, inResearch in Optical Sciences(Optica Publishing Group, 2014) p. QTh1A.2

    work page 2014

  21. [21]

    Giovannetti, S

    V. Giovannetti, S. Lloyd, and L. Maccone, Advances in quantum metrology, Nature photonics5, 222 (2011)

    work page 2011

  22. [22]

    Polino, M

    E. Polino, M. Valeri, N. Spagnolo, and F. Sciarrino, Photonic quantum metrology, AVS Quantum Science2(2020)

    work page 2020

  23. [23]

    J. P. Dowling, Quantum optical metrology–the lowdown on high-n00n states, Contemporary physics49, 125 (2008)

    work page 2008

  24. [24]

    Knill, R

    E. Knill, R. Laflamme, and G. J. Milburn, A scheme for efficient quantum computation with linear optics, nature409, 46 (2001)

    work page 2001

  25. [25]

    Hong, Z.-Y

    C.-K. Hong, Z.-Y. Ou, and L. Mandel, Measurement of subpicosecond time intervals between two photons by interference, Physical review letters59, 2044 (1987)

    work page 2044

  26. [26]

    Wu and H

    J.-Y. Wu and H. F. Hofmann, Evaluation of bipartite entanglement between two optical multi-mode systems using mode translation symmetry, New Journal of Physics19, 103032 (2017)

    work page 2017

  27. [27]

    Kiyohara, N

    T. Kiyohara, N. Yamashiro, R. Okamoto, H. Araki, J.-Y. Wu, H. F. Hofmann, and S. Takeuchi, Direct and efficient verification of entanglement between two multimode–multiphoton systems, Optica7, 1517 (2020)

    work page 2020

  28. [28]

    K. Qian, K. Wang, L. Chen, Z. Hou, M. Krenn, S. Zhu, and X.-s. Ma, Multiphoton non-local quantum interference controlled by an undetected photon, Nature Communications14, 1480 (2023)

    work page 2023

  29. [29]

    K. Wang, Z. Hou, K. Qian, L. Chen, M. Krenn, M. Aspelmeyer, A. Zeilinger, S. Zhu, and X.-S. Ma, Violation of bell inequality with unentangled photons, Science Advances11, eadr1794 (2025)

    work page 2025

  30. [30]

    H. F. Hofmann, Y. Kodama, and J. R. Hance, Implementation of nonlocal multi-photon interference by mode swapping, Proc. SPIE13618, 136180H (2025)

    work page 2025

  31. [31]

    H. M. Wiseman, S. J. Jones, and A. C. Doherty, Steering, entanglement, nonlocality, and the einstein-podolsky-rosen paradox, Phys. Rev. Lett.98, 140402 (2007)

    work page 2007