Heralded Optical Entanglement Generation via the Graph Picture of Linear Quantum Networks

Seungbeom Chin; Marcin Karczewski; Yong-Su Kim

doi:10.22331/q-2024-12-18-1572

Heralded Optical Entanglement Generation via the Graph Picture of Linear Quantum Networks

Seungbeom Chin^1,2,3, Marcin Karczewski^4,2, and Yong-Su Kim^5,6

¹Okinawa Institute of Science and Technology Graduate University, Okinawa 904-0495, Japan
²International Centre for Theory of Quantum Technologies, University of Gdańsk, 80-308, Gdańsk, Poland
³Department of Electrical and Computer Engineering, Sungkyunkwan University, Suwon 16419, Korea
⁴Institute of Spintronics and Quantum Information, Faculty of Physics and Astronomy, Adam Mickiewicz University, Poland
⁵Center for Quantum Information, Korea Institute of Science and Technology (KIST), Seoul, 02792, Korea
⁶Division of Quantum Information Technology, KIST School, Korea University of Science and Technology, Seoul 02792, Korea

Published:	2024-12-18, volume 8, page 1572
Eprint:	arXiv:2310.10291v3
Doi:	https://doi.org/10.22331/q-2024-12-18-1572
Citation:	Quantum 8, 1572 (2024).

Find this paper interesting or want to discuss? Scite or leave a comment on SciRate.

Abstract

Non-destructive heralded entanglement with photons is a valuable resource for quantum information processing. However, they generally entail ancillary particles and modes that amplify the circuit intricacy. To address this challenge, a recent work [16] introduced a graph approach for creating multipartite entanglements with boson subtractions. Nonetheless, it remains an essential intermediate step toward practical heralded schemes: the proposition of heralded subtraction operators in bosonic linear quantum networks. This research establishes comprehensive translation rules from subtraction operators to linear optical operators, which provides a seamless path to design heralded schemes with single photons. Our method begets enhanced or previously unreported schemes for the $N$-partite GHZ state with $2N$ photons, $N$-partite W state with $2N+1$ photons and superposition of $N=3$ GHZ and W states with 9 photons. Our streamlined approach can straightforwardly design heralded schemes for multipartite entangled states by assembling the operators according to the guidence of sculpting bigraphs, hence significantly simplifies the quantum circuit design process.

Featured image: Translation rules from graph elements of the linear quantum graph (LQG) picture to linear optical elements

Popular summary

Quantum entanglement is an amazing resource for all sorts of quantum technologies. But like anything valuable, it doesn’t come for free. One big challenge is to draw blueprints for creating entangled states of intricate multipartite structure. Designing ways to generate these states is no easy task, especially if we want the process to be non-destructive and give us a "heralded" success- meaning we know it worked without ruining the state itself.

In this work, we build on a cutting-edge idea called the linear quantum graph (LQG) picture, which was introduced in Quantum 5, 611 (2021) and expanded in npj Quantum Information 10, 67 (2024). This framework uses graph theory to design entangled states in a neat and efficient way. The earlier work showed how to use a set of spatially overlapped annihilation operators, defined as sculpting operators, to generate heralded multipartite entanglement. All the sculpting operators are represented as bipartite graphs in the LQG picture, and by leveraging the advantageous mathematical properties of the graphs, it found several essential entanglement generation schemes.

On the other hand, one intermediate step that was missing in the previous work is to connect the graphical sculpting operators with the actual heralded circuits. In our current work, we complete the missing link with a systematic procedure for translating these graphical models into practical optical circuits. Once we know such operators, we can automatically design heralded schemes for multipartite entangled states by assembling the operators according to the guidance of sculpting bigraphs. We demonstrate this point by proposing novel schemes for the heralded N-partite GHZ and W states and the superposition of N=3 GHZ and W states. The work emphasizes the versatility of the LQG approach and its capacity to produce various entangled states with fewer resources compared to traditional methods.

► BibTeX data

@article{Chin2024heraldedoptical,
  doi = {10.22331/q-2024-12-18-1572},
  url = {https://doi.org/10.22331/q-2024-12-18-1572},
  title = {Heralded {O}ptical {E}ntanglement {G}eneration via the {G}raph {P}icture of {L}inear {Q}uantum {N}etworks},
  author = {Chin, Seungbeom and Karczewski, Marcin and Kim, Yong-Su},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {8},
  pages = {1572},
  month = dec,
  year = {2024}
}

► References

[1] Martin B Plenio and Shashank Virmani. An introduction to entanglement measures. Quantum Inf. Comput., 7 (1): 1–51, 2007. URL https://doi.org/10.26421/QIC7.1-2-1.
https://doi.org/10.26421/QIC7.1-2-1

[2] John Preskill. Quantum computing and the entanglement frontier. arXiv preprint arXiv:1203.5813, 2012. URL https://doi.org/10.48550/arXiv.1203.5813.
https://doi.org/10.48550/arXiv.1203.5813
arXiv:1203.5813

[3] Nicolas Gisin, Grégoire Ribordy, Wolfgang Tittel, and Hugo Zbinden. Quantum cryptography. Reviews of modern physics, 74 (1): 145, 2002. URL https://doi.org/10.1103/RevModPhys.74.145.
https://doi.org/10.1103/RevModPhys.74.145

[4] Malte C Tichy, Fernando de Melo, Marek Kuś, Florian Mintert, and Andreas Buchleitner. Entanglement of identical particles and the detection process. Fortschritte der Physik, 61 (2-3): 225–237, 2013. URL https://doi.org/10.1002/prop.201200079.
https://doi.org/10.1002/prop.201200079

[5] Mario Krenn, Armin Hochrainer, Mayukh Lahiri, and Anton Zeilinger. Entanglement by path identity. Physical Review Letters, 118 (8): 080401, 2017. URL https://doi.org/10.1103/PhysRevLett.118.080401.
https://doi.org/10.1103/PhysRevLett.118.080401

[6] Pawel Blasiak and Marcin Markiewicz. Entangling three qubits without ever touching. Scientific Reports, 9 (1): 20131, 2019. URL https://doi.org/10.1038/s41598-019-55137-3.
https://doi.org/10.1038/s41598-019-55137-3

[7] Mariana R Barros, Seungbeom Chin, Tanumoy Pramanik, Hyang-Tag Lim, Young-Wook Cho, Joonsuk Huh, and Yong-Su Kim. Entangling bosons through particle indistinguishability and spatial overlap. Optics Express, 28 (25): 38083–38092, 2020. URL https://doi.org/10.1364/OE.410361.
https://doi.org/10.1364/OE.410361

[8] Seungbeom Chin, Yong-Su Kim, and Sangmin Lee. Graph picture of linear quantum networks and entanglement. Quantum, 5: 611, 2021. URL https://doi.org/10.22331/q-2021-12-23-611.
https://doi.org/10.22331/q-2021-12-23-611

[9] Donghwa Lee, Tanumoy Pramanik, Seongjin Hong, Young-Wook Cho, Hyang-Tag Lim, Seungbeom Chin, and Yong-Su Kim. Entangling three identical particles via spatial overlap. Optics Express, 30 (17): 30525–30535, 2022. URL https://doi.org/10.1364/OE.460866.
https://doi.org/10.1364/OE.460866

[10] Jeremy C Adcock, Sam Morley-Short, Joshua W Silverstone, and Mark G Thompson. Hard limits on the postselectability of optical graph states. Quantum Science and Technology, 4 (1): 015010, 2018. URL https://doi.org/10.1088/2058-9565/aae950.
https://doi.org/10.1088/2058-9565/aae950

[11] Stefanie Barz, Gunther Cronenberg, Anton Zeilinger, and Philip Walther. Heralded generation of entangled photon pairs. Nature Photonics, 4 (8): 553–556, 2010. URL https://doi.org/10.1038/nphoton.2010.156.
https://doi.org/10.1038/nphoton.2010.156

[12] Scott B Papp, Kyung Soo Choi, Hui Deng, Pavel Lougovski, SJ Van Enk, and HJ Kimble. Characterization of multipartite entanglement for one photon shared among four optical modes. Science, 324 (5928): 764–768, 2009. URL https://doi.org/10.1126/science.1172260.
https://doi.org/10.1126/science.1172260

[13] Jonas Zeuner, Aditya N Sharma, Max Tillmann, René Heilmann, Markus Gräfe, Amir Moqanaki, Alexander Szameit, and Philip Walther. Integrated-optics heralded controlled-not gate for polarization-encoded qubits. npj Quantum Information, 4 (1): 13, 2018. URL https://doi.org/10.1038/s41534-018-0068-0.
https://doi.org/10.1038/s41534-018-0068-0

[14] Jin-Peng Li, Xuemei Gu, Jian Qin, Dian Wu, Xiang You, Hui Wang, Christian Schneider, Sven Höfling, Yong-Heng Huo, Chao-Yang Lu, et al. Heralded nondestructive quantum entangling gate with single-photon sources. Physical Review Letters, 126 (14): 140501, 2021. URL https://doi.org/10.1103/PhysRevLett.126.140501.
https://doi.org/10.1103/PhysRevLett.126.140501

[15] Dat Thanh Le, Warit Asavanant, and Nguyen Ba An. Heralded preparation of polarization entanglement via quantum scissors. Physical Review A, 104 (1): 012612, 2021. URL https://doi.org/10.1103/PhysRevA.104.012612.
https://doi.org/10.1103/PhysRevA.104.012612

[16] Seungbeom Chin, Yong-Su Kim, and Marcin Karczewski. Shortcut to multipartite entanglement generation: A graph approach to boson subtractions. npj Quantum Information, 10 (1): 67, 2024a. URL https://doi.org/10.1038/s41534-024-00845-6.
https://doi.org/10.1038/s41534-024-00845-6

[17] John van de Wetering. ZX-calculus for the working quantum computer scientist. arXiv preprint arXiv:2012.13966, 2020. URL https://doi.org/10.48550/arXiv.2012.13966.
https://doi.org/10.48550/arXiv.2012.13966
arXiv:2012.13966

[18] Jacob Biamonte. Lectures on quantum tensor networks. arXiv preprint arXiv:1912.10049, 2019. URL https://doi.org/10.48550/arXiv.1912.10049.
https://doi.org/10.48550/arXiv.1912.10049
arXiv:1912.10049

[19] Marc Hein, Wolfgang Dür, Jens Eisert, Robert Raussendorf, M Nest, and H-J Briegel. Entanglement in graph states and its applications. arXiv preprint quant-ph/0602096, 2006. URL https://doi.org/10.48550/arXiv.quant-ph/0602096.
https://doi.org/10.48550/arXiv.quant-ph/0602096
arXiv:quant-ph/0602096

[20] Marcin Karczewski, Su-Yong Lee, Junghee Ryu, Zakarya Lasmar, Dagomir Kaszlikowski, and Paweł Kurzyński. Sculpting out quantum correlations with bosonic subtraction. Physical Review A, 100 (3): 033828, 2019. URL https://doi.org/10.1103/PhysRevA.100.033828.
https://doi.org/10.1103/PhysRevA.100.033828

[21] Lin Htoo Zaw, Zakarya Lasmar, Chi-Huan Nguyen, Ko-Wei Tseng, Dzmitry Matsukevich, Dagomir Kaszlikowski, and Valerio Scarani. Sculpting bosonic states with arithmetic subtractions. New Journal of Physics, 24 (8): 083023, 2022. URL https://doi.org/10.1088/1367-2630/ac8305.
https://doi.org/10.1088/1367-2630/ac8305

[22] Antonio Acín, A Andrianov, L Costa, E Jané, JI Latorre, and Rolf Tarrach. Generalized schmidt decomposition and classification of three-quantum-bit states. Physical Review Letters, 85 (7): 1560, 2000. URL https://doi.org/10.1103/PhysRevLett.85.1560.
https://doi.org/10.1103/PhysRevLett.85.1560

[23] Michael Varnava, Daniel E Browne, and Terry Rudolph. How good must single photon sources and detectors be for efficient linear optical quantum computation? Physical review letters, 100 (6): 060502, 2008. URL https://doi.org/10.1103/PhysRevLett.100.060502.
https://doi.org/10.1103/PhysRevLett.100.060502

[24] FV Gubarev, IV Dyakonov, M Yu Saygin, GI Struchalin, SS Straupe, and SP Kulik. Improved heralded schemes to generate entangled states from single photons. Physical Review A, 102 (1): 012604, 2020. URL https://doi.org/10.1103/PhysRevA.102.012604.
https://doi.org/10.1103/PhysRevA.102.012604

[25] Ş K Özdemir, Eiji Matsunaga, Toshiyuki Tashima, Takashi Yamamoto, Masato Koashi, and Nobuyuki Imoto. An optical fusion gate for W-states. New Journal of Physics, 13 (10): 103003, 2011. URL https://doi.org/10.1088/1367-2630/13/10/103003.
https://doi.org/10.1088/1367-2630/13/10/103003

[26] Ke Li, Dongliang Zheng, Wangqiong Xu, Huibing Mao, and Jiqing Wang. W states fusion via polarization-dependent beam splitter. Quantum Information Processing, 19 (11): 412, 2020. URL https://doi.org/10.1007/s11128-020-02898-w.
https://doi.org/10.1007/s11128-020-02898-w

[27] Michael Walter, David Gross, and Jens Eisert. Multipartite entanglement. Quantum Information: From Foundations to Quantum Technology Applications, pages 293–330, 2016. URL https://doi.org/10.1002/9783527805785.ch14.
https://doi.org/10.1002/9783527805785.ch14

[28] Román Orús. A practical introduction to tensor networks: Matrix product states and projected entangled pair states. Annals of physics, 349: 117–158, 2014. URL https://doi.org/10.1016/j.aop.2014.06.013.
https://doi.org/10.1016/j.aop.2014.06.013

[29] Daniel E Browne and Terry Rudolph. Resource-efficient linear optical quantum computation. Physical Review Letters, 95 (1): 010501, 2005. URL https://doi.org/10.1103/PhysRevLett.95.010501.
https://doi.org/10.1103/PhysRevLett.95.010501

[30] Guilherme Luiz Zanin, Maxime J Jacquet, Michele Spagnolo, Peter Schiansky, Irati Alonso Calafell, Lee A Rozema, and Philip Walther. Fiber-compatible photonic feed-forward with 99% fidelity. Optics Express, 29 (3): 3425–3437, 2021. URL https://doi.org/10.1364/OE.409867.
https://doi.org/10.1364/OE.409867

[31] XuBo Zou and W Mathis. Scheme for optical implementation of orbital angular momentum beam splitter of a light beam and its application in quantum information processing. Physical Review A, 71 (4): 042324, 2005. URL https://doi.org/10.1103/PhysRevA.71.042324.
https://doi.org/10.1103/PhysRevA.71.042324

[32] Nicolas Maring, Andreas Fyrillas, Mathias Pont, Edouard Ivanov, Petr Stepanov, Nico Margaria, William Hease, Anton Pishchagin, Aristide Lemaı̂tre, Isabelle Sagnes, et al. A versatile single-photon-based quantum computing platform. Nature Photonics, pages 1–7, 2024. URL https://doi.org/10.1038/s41566-024-01403-4.
https://doi.org/10.1038/s41566-024-01403-4

[33] H Cao, LM Hansen, F Giorgino, L Carosini, P Zahálka, F Zilk, JC Loredo, and P Walther. Photonic source of heralded greenberger-horne-zeilinger states. Physical Review Letters, 132 (13): 130604, 2024. URL https://doi.org/10.1103/PhysRevLett.132.130604.
https://doi.org/10.1103/PhysRevLett.132.130604

[34] Wan Zo, Seungbeom Chin, and Yong-Su Kim. Heralded optical entanglement distribution via lossy quantum channels: A comparative study. arXiv preprint arXiv:2409.16622, 2024. URL https://doi.org/10.48550/arXiv.2409.16622.
https://doi.org/10.48550/arXiv.2409.16622
arXiv:2409.16622

[35] Seungbeom Chin. From linear quantum system graphs to qubit graphs: Heralded generation of graph states. arXiv preprint arXiv:2306.15148, 2023. URL https://doi.org/10.48550/arXiv.2306.15148.
https://doi.org/10.48550/arXiv.2306.15148
arXiv:2306.15148

[36] Seungbeom Chin, Junghee Ryu, and Yong-Su Kim. Exponentially enhanced scheme for the heralded qudit greenberger-horne-zeilinger state in linear optics. Phys. Rev. Lett., 133: 253601, 2024b. URL https://doi.org/10.1103/PhysRevLett.133.253601.
https://doi.org/10.1103/PhysRevLett.133.253601

[37] Jaroslav Kysela, Xiaoqin Gao, and Borivoje Dakić. Fourier transform of the orbital angular momentum of a single photon. Physical Review Applied, 14 (3): 034036, 2020. URL https://doi.org/10.1103/PhysRevApplied.14.034036.
https://doi.org/10.1103/PhysRevApplied.14.034036

Cited by

[1] 尹华磊 Yin Hualei, 卢旭阳 Lu Xuyang, 张庆航 Zhang Qinghang, and 陈增兵 Chen Zengbing, " 基于融合的量子计算研究进展（特邀）", Laser & Optoelectronics Progress 62 11, 1127003 (2025).

[2] Chon-Fai Kam and En-Jui Kuo, "Quantum-secured device-independent global positioning system", EPJ Quantum Technology 13 1, 18 (2026).

[3] Jia-Heng Ni, Liang Bin, Yi-Hao Kang, Qi-Ping Su, and Chui-Ping Yang, "Efficient scheme for generating a W-type optical entangled cat state", Applied Physics Letters 126 24, 244001 (2025).

[4] Minhyeok Kang, Jaehee Kim, William J Munro, Seungbeom Chin, and Joonsuk Huh, "Heralded linear optical generation of Dicke states", New Journal of Physics 28 5, 054501 (2026).

[5] Imogen Forbes, Farzad Ghafari, Edward C R Deacon, Sukhjit P Singh, Emilien Lavie, Patrick Yard, Reece D Shaw, Anthony Laing, and Nora Tischler, "Heralded generation of entanglement with photons", Reports on Progress in Physics 88 8, 086002 (2025).

[6] Wan Zo, Seungbeom Chin, and Yong-Su Kim, "Heralded optical entanglement distribution via lossy quantum channels: a comparative study", Optics Express 33 6, 12459 (2025).

[7] Eneet Kaur, Ashlesha Patil, and Saikat Guha, "Resource-efficient loss-aware photonic-graph-state preparation using atomic emitters", Physical Review A 112 6, 062608 (2025).

[8] Fumihiro Kaneda and Masahiro Yabuno, "Active multiplexing for scalable generation and manipulation of photonic quantum states", Nano Convergence 13 1, 10 (2026).

[9] Seungbeom Chin, Yong-Su Kim, and Marcin Karczewski, "Shortcut to multipartite entanglement generation: A graph approach to boson subtractions", npj Quantum Information 10 1, 67 (2024).

[10] Matteo Piccolini, Marcin Karczewski, Andreas Winter, and Rosario Lo Franco, "Robust generation of N-partite N-level singlet states by identical particle interferometry", Quantum Science and Technology 10 1, 015013 (2025).

[11] Seungbeom Chin, Junghee Ryu, and Yong-Su Kim, "Exponentially Enhanced Scheme for the Heralded Qudit Greenberger-Horne-Zeilinger State in Linear Optics", Physical Review Letters 133 25, 253601 (2024).

[12] Kobra Mahdavipour, Farzam Nosrati, Stefania Sciara, Roberto Morandotti, and Rosario Lo Franco, "Generation of genuine multipartite entangled states via indistinguishability of identical particles", arXiv:2403.17171, (2024).

[13] Kobra Mahdavipour, Farzam Nosrati, Stefania Sciara, Roberto Morandotti, and Rosario Lo Franco, "Generation of Genuine Multipartite Entangled States via Indistinguishability of Identical Particles", PRX Quantum 5 4, 040350 (2024).

[14] Seungbeom Chin, "Creating highly symmetric qudit heralded entanglement through highly symmetric graphs", arXiv:2404.05273, (2024).

The above citations are from Crossref's cited-by service (last updated successfully 2026-08-09 14:09:33) and SAO/NASA ADS (last updated successfully 2026-08-09 14:09:34). The list may be incomplete as not all publishers provide suitable and complete citation data.

This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions.