The DOI matches its Crossref record; 33 of the 33 references it cites were found in a registry or an index.
De Broglie wavelength of a non-local four-photon state
Open accessAbstract
Superposition is one of the most distinctive features of quantum theory and has been demonstrated in numerous single-particle interference experiments. Quantum entanglement, the coherent superposition of states in multi-particle systems, yields more complex phenomena. One important type of multi-particle experiment uses path-entangled number states, which exhibit pure higher-order interference and the potential for applications in metrology and imaging; these include quantum interferometry and spectroscopy with phase sensitivity at the Heisenberg limit, or quantum lithography beyond the classical diffraction limit. It has been generally understood that in optical implementations of such schemes, lower-order interference effects always decrease the overall performance at higher particle numbers. Such experiments have therefore been limited to two photons. Here we overcome this limitation, demonstrating a four-photon interferometer based on linear optics. We observe interference fringes with a periodicity of one-quarter of the single-photon wavelength, confirming the presence of a four-particle mode-entangled state. We anticipate that this scheme should be extendable to arbitrary photon numbers, holding promise for realizable applications with entanglement-enhanced performance.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
The source backs part of the claim, not all of it — or backs it for a different population, condition or comparison.
In the citing paper
“It was experimentally realized for N = 3 (Mitchell, Lundeen, and Steinberg, 2004) and N = 4 (Walther et al., 2004) (see also other related experiments, Rarity et al., 1990b;Edamatsu et al., 2002;Sun et al., 2006;Nagata et al., 2007).”
From Multiphoton entanglement and interferometry (2012) · cites this paper as Walther et al., 2004
Experimental — accuracy not yet measuredIn the citing paper
“However, the experimental preparation of NOON states with large N is extremely challenging, and to date only N=3, 4 and 5 photonic NOON states have been reported2345.”
From Photonic polarization gears for ultra-sensitive angular measurements (2013) · cites this paper as [3]
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cites
Measurement of subpicosecond time intervals between two photons by interference
Hong, C. K., Ou, Z. Y., & Mandel, L. (1987) · Physical Review Letters · doi:10.1103/physrevlett.59.2044 · Cited by 4,369
Die gegenw�rtige Situation in der Quantenmechanik
Schr�dinger, E. (1935) · Die Naturwissenschaften · doi:10.1007/bf01491891 · Cited by 3,392
New High-Intensity Source of Polarization-Entangled Photon Pairs
Kwiat, P. G., Mattle, K., Weinfurter, H., Zeilinger, A., Sergienko, A. V., & Shih, Y. (1995) · Physical Review Letters · doi:10.1103/physrevlett.75.4337 · Cited by 3,102
Self-citationQuantum Interferometric Optical Lithography: Exploiting Entanglement to Beat the Diffraction Limit
Boto, A. N., Kok, P., Abrams, D. S., Braunstein, S. L., Williams, C. P., & Dowling, J. P. (2000) · Physical Review Letters · doi:10.1103/physrevlett.85.2733 · Cited by 1,494
Wave–particle duality of C60 molecules
Arndt, M., Nairz, O., Voss-Andreae, J., Keller, C., van der Zouw, G., & Zeilinger, A. (1999) · Nature · doi:10.1038/44348 · Cited by 1,255
Self-citationOptimal frequency measurements with maximally correlated states
Bollinger, J. J., Itano, W. M., Wineland, D. J., & Heinzen, D. J. (1996) · Physical Review A · doi:10.1103/physreva.54.r4649 · Cited by 1,167
Shih, Y. H., & Alley, C. O. (1988) · Physical Review Letters · doi:10.1103/physrevlett.61.2921 · Cited by 917
Violation of Bell's Inequality and Classical Probability in a Two-Photon Correlation Experiment
Ou, Z. Y., & Mandel, L. (1988) · Physical Review Letters · doi:10.1103/physrevlett.61.50 · Cited by 879
Interferometric detection of optical phase shifts at the Heisenberg limit
Holland, M., & Burnett, K. R. (1993) · Physical Review Letters · doi:10.1103/physrevlett.71.1355 · Cited by 864
Keith, D. W., Ekstrom, C. R., Turchette, Q. A., et al. (1991) · Physical Review Letters · doi:10.1103/physrevlett.66.2693 · Cited by 583
Flagged first, then by citations
Research works printed but not linked: 1
- Lee, H., Kok, P. & Dowling, J. P. in Proc. Sixth Int. Conf. on Quantum Communication, Measurement and Computing (eds Shapiro, J. H. & Hirota, O.) 223–229 (Rinton Press, Princeton, 2002)
Cited by
Sorted by citations
Items 501–555 of 555
Universal Model for Multi-mode NOON State Generation Using Fock State Filters
Zhang, L., & Chan, K. W. C. (2018) · Conference on Lasers and Electro-Optics Pacific Rim (CLEO-PR) · doi:10.1364/cleopr.2018.w3a.112
Efficient quantum logic circuits: or, How I Learned to Stop Worrying and Love Hilbert Space
White, A. G., de Almeida, M. P., Barbieri, M., Biggerstaff, D. N., Dalton, R. B., Gilchrist, A., Gillett, G., James, D. F. V., Langford, N. K., Lanyon, B. P., et al. (2007) · International Conference on Quantum Information · doi:10.1364/icqi.2007.ifb3
Nonlinear spectroscopy with entangled photons; manipulating quantum pathways of matterPreprint
Marx, O. R. C. A., & Mukamel, S. (2009) · arXiv (Cornell University) · doi:10.48550/arxiv.0902.2549
Peniakov, G., Su, Z.-E., Beck, A., Amar, O., Ryzhkov, M., & Gershoni, D. (2019) · The Rochester Conferences on Coherence and Quantum Optics and the Quantum Information and Measurement meeting · doi:10.1364/cqo.2019.m5a.17
Peniakov, G., Su, Z.-E., Beck, A., et al. (2019) · doi:10.1364/fio.2019.fm5e.4
Quantum-enhanced Phase Estimation in Optical Interferometry
Sahota, J. (2017) · TSpace (University of Toronto)
Byoung Seung, H. A. M. (2020) · arXiv (Cornell University) · doi:10.48550/arxiv.2009.02665
Controlling parameter estimation precision by designing the spin environment
Hu, J., Ke, Q., & Ji, Y. (2020) · Optik · doi:10.1016/j.ijleo.2020.165754
Super-Sensitive Quantum Metrology without Many-Photon Entanglement
Lahiri, M., & Erhard, M. (2020) · Frontiers in Optics · doi:10.1364/fio.2020.jm6a.22
Deterministic quantum correlation in an interferometric schemePreprint
Byoung Seung, H. A. M. (2020) · arXiv (Cornell University) · doi:10.48550/arxiv.2012.09387
Macroscopically entangled light fields: A quantum laserPreprint
Byoung Seung, H. A. M. (2021) · arXiv (Cornell University) · doi:10.48550/arxiv.2102.04659
Byoung Seung, H. A. M. (2021) · arXiv (Cornell University) · doi:10.48550/arxiv.2102.11682 · Cited by 1
Macroscopic randomness for quantum entanglement generationPreprint
Byoung Seung, H. A. M. (2021) · arXiv (Cornell University) · doi:10.48550/arxiv.2103.02879
Direct observation of photon bunching in thermal light in quantum Fourier transform spectroscopyPreprint
Zhang, D. (2021) · arXiv (Cornell University) · doi:10.48550/arxiv.2103.03419 · Cited by 1
High-visibility classical multi-photon interference
Agafonov, I. N., Chekhova, M. V., & Iskhakov, T. S. (2007) · Conference on Lasers and Electro-Optics · doi:10.1109/cleo.2007.4453452
Tephanie, B. Y. S., Immons, S., Ohn, J., & Orton, J. L. M. (2012)
Kim, S., & Byoung Seung, H. A. M. (2021) · Research Square · doi:10.21203/rs.3.rs-798613/v1 · Cited by 2
Deterministic quantum correlation between coherently paired photons acting on a beam splitterPreprint
Byoung Seung, H. A. M. (2021) · arXiv (Cornell University) · doi:10.48550/arxiv.2108.09596
Quantum Fourier transform spectroscopy of biexcitonPreprint
Seki, H., Miyajima, K., & Shimizu, R. (2021) · arXiv (Cornell University) · doi:10.48550/arxiv.2109.03715
Beating the classical phase precision limit using a quantum neuromorphic platformPreprint
Krisnanda, T., Ghosh, S., Paterek, T., et al. (2021) · arXiv (Cornell University) · doi:10.48550/arxiv.2110.07507
A quantum ring gyroscope based on coherence de Broglie wavesPreprint
Byoung Seung, H. A. M. (2021) · arXiv (Cornell University) · doi:10.48550/arxiv.2111.03224
By Using Number State Filtered Coherent States to Improve Phase Sensitivity with Multiple Passes
Xia, L.-X., Lan, Y., Rusul, A., & Niyazi, Y. (2022) · Lecture notes in electrical engineering · doi:10.1007/978-981-16-4258-6_31
One hundred years of the photon
Milant’ev, V. P. (2005) · Uspekhi Fizicheskih Nauk · doi:10.3367/ufnr.0175.200511g.1233
(2019) · Elsevier eBooks · doi:10.1016/b978-0-12-816081-7.09986-1
Matthews, J. C. F. (2012) · Springer theses · doi:10.1007/978-3-642-32870-1_1
Syouji, A., Shimizu, R., Nagano, S., Suizu, K., & Edamatsu, K. (2023) · Japanese Journal of Applied Physics · doi:10.35848/1347-4065/acb874
Xiaoju, 任. R., Huili, 郑. Z., Zezhun, 时. S., & GuangRi, 金. J. (2023) · Acta Optica Sinica · doi:10.3788/aos221563
Boosted Binary Quantum Classifier via Graphical Kernel
Cai, Y., & Huang, D. (2023) · Entropy · doi:10.3390/e25060870
The controversy about interference of photons
Bhatta, V. S. (2024) · Studies in History and Philosophy of Science Part A · doi:10.1016/j.shpsa.2024.06.003
Optimal probe states for phase estimation with a fixed mean particle number
Qin, J.-F., & Liu, B. (2025) · Communications in Theoretical Physics · doi:10.1088/1572-9494/adac3c
Enhanced phase-based plasmonic biosensing with quantum states of light
Mpofu, K. T., & Mthunzi-Kufa, P. T. (2025) · Journal of Physics Conference Series · doi:10.1088/1742-6596/2970/1/012012
Byoung Seung, H. A. M. (2025) · Scientific Reports · doi:10.1038/s41598-025-95739-8 · Cited by 1
Engineering nonlinear boson-boson interactions using mediating spin systems
McAleese, H., Paternostro, M., & Puebla, R. (2025) · Physical Review Research · doi:10.1103/physrevresearch.7.023253 · Cited by 2
Brooks, R., Maggio, L., Jaeken, T., Ho, J., Gauger, E. M., Tamma, V., & Fedrizzi, A. (2026) · Physical Review Letters · doi:10.1103/6xy6-c2yd · Cited by 2
24 38Nanolithographie und Strukturierung
Hartmann, U. (2025) · De Gruyter eBooks · doi:10.1515/9783486855449-002
Interference of overlap-free entangled photons with a Mach-Zehnder-like interferometerPreprint
Jin, X., Peng, C., Yang, T., & Deng, Y. (2010) · arXiv (Cornell University) · doi:10.48550/arxiv.1005.0802
Byoung Seung, H. A. M. (2025) · OSA Advanced Photonics Congress · doi:10.1364/noma.2025.noth3c.4
Cavity-enhanced Photon-Photon Interactions With Bright Quantum Dot Sources
Giesz, V. (2015) · theses.fr (ABES) · doi:10.70675/15df0630z7cfaz4b74za464z5ba4bac2e6b7 · Cited by 1
Solutions évolutives pour les réseaux de communication quantique
Fedrici, B. (2017) · theses.fr (ABES) · doi:10.70675/4ee6f82ez8faez4962z907cz3c032c4ee820
Detecting strongly non-Gaussian entanglement
Deside, S., Haas, T., & Cerf, N. J. (2026) · Physical Review Research · doi:10.1103/297d-3tbj · Cited by 1
Single photon generation and manipulation with semiconductor quantum dot devices
Santis, L. D. (2018) · theses.fr (ABES) · doi:10.70675/5fbfc2e0z4653z436dza99dz0913e16f21ca · Cited by 2
Towards quantum applications based on photonic entanglement
Vergyris, P. (2017) · theses.fr (ABES) · doi:10.70675/8ff84404zfa1ez495dz890fz44136f964456
Mazeas, F. (2018) · theses.fr (ABES) · doi:10.70675/aa672be9z2ac8z4534z8448zfbe5c47f56e5
Kim, S., & Byoung Seung, H. A. M. (2026) · Research Square · doi:10.21203/rs.3.rs-9237545/v1
Byoung Seung, H. A. M. (2026) · Research Square · doi:10.21203/rs.3.rs-9215675/v1
Dose-efficient quantum phase estimation in lossy optical interferometry
Yu, Q., Wang, B., zheng, K., Mi, M., Li, H. D., & Zhang, L. (2026) · Optica · doi:10.1364/optica.595738 · Cited by 3
Versatile on-chip reconfigurable two-photon interference platforms using thin-film lithium niobate
Choi, M., Kim, C., Moon, S., Hwang, H., Seo, M., Lim, H., Chung, H., Jung, H., & Kwon, H. (2026) · APL Photonics · doi:10.1063/5.0315916
Correlation properties of non-classical light fields and their applications in imaging
Yan, Y., Li, J., Han, S., Liu, Z., Guo, C., Hu, J., Qin, C., & Xiao, L. (2026) · Photonics Insights · doi:10.3788/pi.2026.r08
Three‐Photon High‐Order Orbital Angular Momentum NOON States for Sub‐Shot‐Noise Angular Measurement
Li, H., Lou, Y.-C., Zhu, W.-Z., Qing, Z., Wang, J., Xue, S.-T., Huang, S., Xu, J. F., Ren, Z., Zhang, L., et al. (2026) · Laser & Photonics Review · doi:10.1002/lpor.71566
Tong, X., He, Z., Zhang, Y., Liu, W., Huang, C.-Y., & Wang, L. V. (2026) · Science Advances · doi:10.1126/sciadv.aea9457
Squeezing-enhanced phase measurement with ternary-binning post-processing
Li, J., he, J., Liu, K., & Gao, J. (2026) · Optics Continuum · doi:10.1364/optcon.608948
A Quantum Wavemeter Using Coherence de Broglie Wavelength in a Single Mach-Zehnder Interferometer
Byoung Seung, H. A. M. (2026) · IEEE/LEOS Summer Topical Meetings · doi:10.1109/sum69529.2026.11660095
Demonstrations of scalable photonic de Broglie wavelengths using a phase-controlled SLM
Byoung Seung, H. A. M. (2026) · Journal of Physics Conference Series · doi:10.1088/1742-6596/3285/1/012001
Applications and characterisation of correlations in quantum optics
Kothe, C. (2011) · KTH Publication Database DiVA (KTH Royal Institute of Technology)
Metadata
- Authors
- Walther, P., Pan, J.-W., Aspelmeyer, M., Ursin, R., Gasparoni, S., & Zeilinger, A.
- Affiliations
- University of Vienna (AT)
- Corresponding author
- Zeilinger, Anton
- Venue
- Nature
- Published
- 2004-05
- Volume
- 429
- Issue
- 6988
- Pages
- 158-161
- ISSN
- 0028-0836 (ISSN-L)
- 1476-4687
- OpenAlex
- W2092899947
- Semantic Scholar
- ea80019dc85701445960d76c6893f2b6a403c5dd
- Cited by
- 555
- References
- 33
- Citations by year
- 2026: 13 · 2025: 18 · 2024: 23 · 2023: 18 · 2022: 16 · 2021: 31 · 2020: 27 · 2019: 24 · 2018: 21 · 2017: 30 · 2016: 30 · 2015: 13 · 2014: 21 · 2013: 23 · 2012: 30
- FWCI
- 28.07
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Licence
- www.springer.com/tdm (tdm)
- Locations
- Nature (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- RePEc: Research Papers in Economics (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Information and Cryptography
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum optics and atomic interactions
- Keywords
- higher-order interference, mode entanglement, quantum metrology, quantum lithography, Heisenberg limit
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
