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12-Photon Entanglement and Scalable Scattershot Boson Sampling with Optimal Entangled-Photon Pairs from Parametric Down-Conversion
Open accessAbstract
Entangled-photon sources with simultaneously near-unity heralding efficiency and indistinguishability are the fundamental elements for scalable photonic quantum technologies. We design and realize a degenerate telecommunication wavelength entangled-photon source from an ultrafast pulsed laser pumped spontaneous parametric down-conversion (SPDC), which shows simultaneously 97% heralding efficiency and 96% indistinguishability between independent single photons without narrow-band filtering. Such a beamlike and frequency-uncorrelated SPDC source allows generation of the first 12-photon genuine entanglement with a state fidelity of 0.572±0.024. We further demonstrate a blueprint of scalable scattershot boson sampling using 12 SPDC sources and a 12×12 mode interferometer for three-, four-, and five-boson sampling, which yields count rates more than 4 orders of magnitude higher than all previous SPDC experiments.
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TL;DR
The paper reports an optimized ultrafast-pumped SPDC entangled-photon source with simultaneously near-unity heralding efficiency and indistinguishability, enabling the first 12-photon genuine entanglement and a scalable scattershot boson sampling blueprint. Using 12 SPDC sources and a 12×12-mode interferometer, it demonstrates three-, four-, and five-boson sampling with multi-photon count rates more than four orders of magnitude higher than previous SPDC experiments.
Key findings
- The source achieved ~97% corrected heralding efficiency and ~96% indistinguishability between independent single photons; Hong-Ou-Mandel interference showed a raw visibility of 0.962 ± 0.011, spectral purity was 0.99, and Bell-state visibility was above 0.997.
- The first 12-photon genuine entanglement was generated with population P = 0.732 ± 0.024, coherence C = 0.419 ± 0.041, and state fidelity reported as 0.572 ± 0.024 in the abstract (0.576 ± 0.024 in the main text), exceeding the 0.5 threshold by more than 3 standard deviations.
- Scattershot boson sampling with 12 SPDC sources and a 12×12-mode interferometer measured three-, four-, and five-photon sampling rates of 3.9 kHz, 44 Hz, and 0.3 Hz, respectively; the 3-boson sampling gave similarity 0.982 ± 0.004 and distance 0.122 ± 0.018.
- The 3.9 kHz three-photon count rate is more than four orders of magnitude higher than the best previous SPDC-based boson sampling experiments and comparable to state-of-the-art quantum-dot single-photon work.
Methods
- The entangled-photon source used beam-like type-II SPDC in a 6.3-mm BBO crystal pumped by a 775-nm pulsed laser with 5.5-nm bandwidth and 80-MHz repetition, generating photon pairs around 1550 nm; YVO4 beam displacers, half-wave plates, dispersion-compensating prisms, 30-nm bandpass filters, and superconducting nanowire single-photon detectors with ~75% average efficiency were used.
- For 12-photon entanglement, six BBO crystals produced six entangled pairs; one photon from each pair was combined on five polarization beam splitters, and 12-photon coincidences were post-selected and measured with wave plates, PBSs, and 24 SNSPDs at 1.8 W pump power and 0.55-mm focal waist, giving a 2.0 MHz two-photon rate and about one 12-photon coincidence per hour.
- For scattershot boson sampling, 12 SPDC sources fed a 12×12-mode interferometer encoded in spatial and polarization modes; idler photons heralded signal photons, and the experiment used a 0.8-mm pump waist and 0.5 MHz two-photon count rate, with similarity/distance metrics and likelihood ratio tests against a distinguishable-photon hypothesis.
Limitations
- The paper states that scaling to larger photon numbers is prohibited by the intrinsically probabilistic generation of entangled photon pairs in SPDC, which would require multiplexing.
- The paper states that similarity/distance characterization is not scalable to larger photon numbers; for four- and five-boson sampling the input-output combinations reach 495×495 and 792×792, making counting events extremely scarce, so a likelihood ratio test was used instead.
- The paper notes that the slight deviation of the measured HOM visibility from the predicted 0.99 could be caused by residual dispersion of the pump laser; the text also makes evident that the 12-photon coincidence rate was about one per hour and the five-boson sampling rate was 0.3 Hz.
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A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“and comparable to the work using state-of-the-art quantum-dot single photons”
§ 2-photon entanglement and scalable scattershot boson sampling with optimal entangled-photon pairs from parametric down-conversion > Abstract
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesThe paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“This high-performance entangled photon source immediately makes it possible to perform the first 12-photon entanglement experiment.”
- Also stated in: § Abstract · plain
“Such a highefficiency and frequency-uncorrelated SPDC source allows generation of the first 12-photon genuine entanglement”
§ 2-photon entanglement and scalable scattershot boson sampling with optimal entangled-photon pairs from parametric down-conversion > Abstract
Load-bearingStrength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passes- Rests on an assumption: The lack of a perfect entangled-photon source is the main reason scalable multi-photon entanglement remained challenging.
- Also stated in: § Abstract · plain
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“From Fig. 3b, we calculate 0.419 0.041 C .”
§ 2-photon entanglement and scalable scattershot boson sampling with optimal entangled-photon pairs from parametric down-conversion > Abstract
Load-bearingStrength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesA result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“From Fig. 3a, we extract the population 0.732 0.024 P .”
§ 2-photon entanglement and scalable scattershot boson sampling with optimal entangled-photon pairs from parametric down-conversion > Abstract
Load-bearingStrength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesA result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“which exceeds the threshold 0.5 more than 3 standard deviations”
§ 2-photon entanglement and scalable scattershot boson sampling with optimal entangled-photon pairs from parametric down-conversion > Abstract
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesA result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“We design and realize a degenerate entangled-photon source from an ultrafast pulsed laser pumped spontaneous parametric downconversion (SPDC), which show simultaneously ~97% heralding efficiency and ~96% indistinguishability between independent single photons.”
- Also stated in: § Abstract · plain
“Here, we design and experimentally realize an optimal SPDC source of entangled photons at telecommunication wavelength by combining the techniques of frequencyuncorrelated and beam-like SPDC.”
§ 2-photon entanglement and scalable scattershot boson sampling with optimal entangled-photon pairs from parametric down-conversion > Abstract
Load-bearingStrength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passes- Rests on an assumption: Near-unity heralding efficiency and indistinguishability are fundamental requirements for scalable photonic quantum technologies.
- Also stated in: § Abstract · plain
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“At a pump beam waist of 1.9 mm, the brightness decreases to 170 Hz/mW whereas the heralding efficiency increases to 94%.”
§ 2-photon entanglement and scalable scattershot boson sampling with optimal entangled-photon pairs from parametric down-conversion > Abstract
Load-bearingStrength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIn the paper
“the measured 3.9 kHz three-photon count rate is more than 4 orders of magnitudes higher than the best previous boson sampling experiments based on SPDC [26][27][28][29]50]”
§ 2-photon entanglement and scalable scattershot boson sampling with optimal entangled-photon pairs from parametric down-conversion > Abstract
What the sources say
- Not matchedcites [26][27][28][29]50]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
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In the paper
“at zero delay the four-fold coincidence count shows a dip with a raw visibility of 0.962 0.011 , without using inefficient narrowband spectral filtering.”
§ 2-photon entanglement and scalable scattershot boson sampling with optimal entangled-photon pairs from parametric down-conversion > Abstract
Load-bearingStrength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesThe paper states this without a source or data behind it here, so there is nothing to check it against. The quote shows it is in the paper.
In the paper
“Subtracting the channel loss in the optical path from the BBO to the single-mode fiber, we estimate a corrected heralding efficiency of 97% at 1.9-mm waist.”
§ 2-photon entanglement and scalable scattershot boson sampling with optimal entangled-photon pairs from parametric down-conversion > Abstract
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- It may state two separate claims as one. 6
- Probably not a substantial claim. 5
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“We measure the three-, four-and five-photon sampling rate of 3.9 kHz, 44 Hz and 0.3 Hz, respectively.”
§ 2-photon entanglement and scalable scattershot boson sampling with optimal entangled-photon pairs from parametric down-conversion > Abstract
Load-bearingStrength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
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In the paper
“at a pump beam waist of 260 μm, we obtain a two-photon count rate of 7100 Hz/mW and a heralding efficiency of 85%.”
§ 2-photon entanglement and scalable scattershot boson sampling with optimal entangled-photon pairs from parametric down-conversion > Abstract
Load-bearingStrength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
A result the paper reports from its own data — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“we obtain a similarity of 0.982 0.004 and a distance of 0.122 0.018 .”
§ 2-photon entanglement and scalable scattershot boson sampling with optimal entangled-photon pairs from parametric down-conversion > Abstract
Load-bearingStrength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
In the paper
“using a BBO crystal with a thickness of 6.3 mm, pump laser wavelength of 775 nm (generating photon pairs centered around 1550 nm), and pulsed laser bandwidth of 5.5 nm [46].”
§ 2-photon entanglement and scalable scattershot boson sampling with optimal entangled-photon pairs from parametric down-conversion > Abstract
What the sources say
- Not matchedcites [46]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
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In the paper
“There are 220, 495 and 792 different no-collision input combinations for the three-, four-and fivephoton boson sampling, which implies that our scattershot boson sampling is expected to yield 220, 495 and 792 times enhancement of the efficiency over standard boson sampling, respectively.”
§ 2-photon entanglement and scalable scattershot boson sampling with optimal entangled-photon pairs from parametric down-conversion > Abstract
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
None of the sources cited for this claim could be matched to a paper in Crossref, so there is nothing to check it against.
In the paper
“In the past two decades, the number of genuinely multi-particle entangled photons from SPDC has been increased up to ten [15,16].”
§ 2-photon entanglement and scalable scattershot boson sampling with optimal entangled-photon pairs from parametric down-conversion > Abstract
What the sources say
- Not matchedcites [15]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
- Not matchedcites [16]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
Strength:plain· not yet calibratedCausal:direct· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it.
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In the paper
“opening up a promising pathway to scalable photonic quantum technologies.”
§ 2-photon entanglement and scalable scattershot boson sampling with optimal entangled-photon pairs from parametric down-conversion > Abstract
Tests✓ Asserted: passes✗ Checkable: fails✓ Load-bearing: passes✓ Based: passesProbably not a substantial claim. It may be too vague to check against evidence.
- Rests on an assumption: Near-unity heralding efficiency and indistinguishability are fundamental requirements for scalable photonic quantum technologies.
What the paper did — it cites no source for this, so there is none to check. The quote shows it is in the paper.
In the paper
“due to the group delay dispersion of the YVO4 crystals (310 fs 2 /mm) and the BBO crystals (79 fs 2 /mm), we employ four pairs of dispersion-compensating prisms to eliminate the dispersion.”
§ 2-photon entanglement and scalable scattershot boson sampling with optimal entangled-photon pairs from parametric down-conversion > Abstract
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesProbably not a substantial claim.
A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Our SPDC source is also readily to be combined with multiplexing to overcome its probabilistic scaling, opening up a new pathway towards scalable photonic quantum technologies.”
§ 2-photon entanglement and scalable scattershot boson sampling with optimal entangled-photon pairs from parametric down-conversion > Abstract
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesProbably not a substantial claim.
- Rests on an assumption: Near-unity heralding efficiency and indistinguishability are fundamental requirements for scalable photonic quantum technologies.
In the paper
“Spontaneous parametric down-conversion (SPDC) [1] has been the most widely used workhorse for producing entangled-photon pairs”
§ 2-photon entanglement and scalable scattershot boson sampling with optimal entangled-photon pairs from parametric down-conversion > Abstract
What the sources say
- Not matchedcites [1]
Couldn’t be matched to a paper in Crossref, so it can’t be checked.
Strength:plain· not yet calibratedTests✓ Asserted: passes✓ Checkable: passes✗ Load-bearing: fails✓ Based: passesProbably not a substantial claim. The paper’s conclusions may not depend on it.
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A conclusion the paper draws from its own results — it cites no other source for it, so there is none to check. The quote shows it is in the paper.
In the paper
“Our work immediately enables high-efficiency implementations of multiplexing, scattershot boson sampling, and heralded creation of remotely entangled photons”
§ 2-photon entanglement and scalable scattershot boson sampling with optimal entangled-photon pairs from parametric down-conversion > Abstract
Tests✓ Asserted: passes✓ Checkable: passes✓ Load-bearing: passes✓ Based: passesIt may state two separate claims as one.
- Rests on an assumption: Near-unity heralding efficiency and indistinguishability are fundamental requirements for scalable photonic quantum technologies.
The paper relies on this without support.
Near-unity heralding efficiency and indistinguishability are fundamental requirements for scalable photonic quantum technologies.
“Entangled photon sources with simultaneously near-unity heralding efficiency and indistinguishability are the fundamental elements for scalable photonic quantum technologies.”
The paper relies on this without support.
The lack of a perfect entangled-photon source is the main reason scalable multi-photon entanglement remained challenging.
“Yet, a more scalable implementation remained challenging, largely to the lack of a perfect entangled-photon source produced by ultrafast laser pumped SPDC where the photonic entanglement fidelity, the collection efficiency, and the indistinguishability between independent photons are simultaneously engineered to close to unity.”
The paper relies on this without support.
The simultaneous combination of near-unity entanglement fidelity, indistinguishability, and collection efficiency remained an outstanding goal before this work.
“There has been important progress in preparing heralded single photons in frequencyuncorrelated pure quantum state [42][43][44], yet the simultaneous combination of nearunity entanglement fidelity, indistinguishability, and collection efficiency remained an outstanding goal.”
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In the citing paper
“While photonic experiments in bulk-optics continue to deliver significant results [15], large-scale quantum information processing with hundreds or thousands of photons will almost certainly require the technological functionalities and scaling that only integrated photonics can provide.”
From Integrated photonic quantum technologies (2020) · cites this paper as [15]
In the citing paper
“It has been demonstrated first on chip via bulk-optic SPDC-SPSs [15, 97] ( Fig.5a ), and recently via a fully integrated chip via SFWM-SPSs [98].”
From Integrated photonic quantum technologies (2020) · cites this paper as [15]
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Percentages, sums and reported differences re-computed from the paper’s own numbers.
Each contradiction between two passages listed here was confirmed by an independent check.
Hong-Ou-Mandel citation points to the wrong reference
MinorThe text cites reference 47 for Hong-Ou-Mandel interference, but the bibliography lists the Hong, Ou, and Mandel paper as reference 46; reference 47 is a different paper.
“we perform a Hong-Ou-Mandel quantum interference [47] between two independent SPDC photons.”
“46. C. K. Hong, Z. Y. Ou, and L. Mandel, Phys. Rev. Lett. 59, 2044 (1987). 47. O. Gühne and G. Tóth, Physics Reports 474, 1 (2009).”
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Experimental scattershot boson sampling
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High-efficiency single-photon generation via large-scale active time multiplexingPreprint
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Flagged first, then by citations
Research works printed but not linked: 1
- 10.4086/toc.2013.v009a004 · DOI
Cited by
Sorted by citations
Quantum computational advantage using photons
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Self-citationQuantum computational chemistry
McArdle, S., Endo, S., Aspuru-Guzik, A., Benjamin, S. C., & Yuan, X. (2020) · Reviews of Modern Physics · doi:10.1103/revmodphys.92.015003 · Cited by 1,621
Integrated photonic quantum technologies
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Forbes, A., Oliveira, M. D., & Dennis, M. R. (2021) · Nature Photonics · doi:10.1038/s41566-021-00780-4 · Cited by 1,422
Advances in high-dimensional quantum entanglement
Erhard, M., Krenn, M., & Zeilinger, A. (2020) · Nature Reviews Physics · doi:10.1038/s42254-020-0193-5 · Cited by 695
Metadata
- Authors
- Zhong, H.-S., Li, Y., Li, W., Peng, L.-C., Su, Z.-E., Hu, Y., He, Y.-M., Ding, X., Zhang, W., Li, H., Zhang, L., Wang, Z., You, L., Wang, X.-L., Jiang, X., Li, L., Chen, Y.-A., Liu, N.-L., Lu, C.-Y., & Pan, J.-W.
- Affiliations
- University of Science and Technology of China (CN)
- Chinese Academy of Sciences (CN)
- ORCID
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 2018-12-21
- Volume
- 121
- Issue
- 25
- Pages
- 250505-250505
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W2896439086
- Cited by
- 432
- References
- 59
- Citations by year
- 2026: 45 · 2025: 54 · 2024: 60 · 2023: 56 · 2022: 58 · 2021: 59 · 2020: 62 · 2019: 35 · 2018: 3
- FWCI
- 18.86
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review Letters (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- Figshare (submittedVersion, cc-by)
- arXiv (Cornell University)
- Bulletin of the American Physical Society
- Funders
- National Natural Science Foundation of China (91836303)
- Chinese Academy of Sciences
- National Fundamental Research Program
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Information and Cryptography
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum optics and atomic interactions
- Keywords
- entangled photon pairs, spontaneous parametric down-conversion, heralding efficiency, photon indistinguishability, photonic quantum technologies
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.
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