Local and scalable detection of genuine multipartite single-photon path entanglement

Patrik Caspar1, Enky Oudot2, Pavel Sekatski1, Nicolas Maring1, Anthony Martin1, Nicolas Sangouard3, Hugo Zbinden1, and Rob Thew1

1Department of Applied Physics, University of Geneva, CH-1211 Genève, Switzerland
2ICFO - Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain
3Institut de physique théorique, Université Paris Saclay, CEA, CNRS, F-91191 Gif-sur-Yvette, France

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Abstract

How can a multipartite single-photon path-entangled state be certified efficiently by means of local measurements? We address this question by constructing an entanglement witness based on local photon detections preceded by displacement operations to reveal genuine multipartite entanglement. Our witness is defined as a sum of three observables that can be measured locally and assessed with two measurement settings for any number of parties $N$. For any bipartition, the maximum mean value of the witness observable over biseparable states is bounded by the maximum eigenvalue of an $N\times N$ matrix, which can be computed efficiently. We demonstrate the applicability of our scheme by experimentally testing the witness for heralded 4- and 8-partite single-photon path-entangled states. Our implementation shows the scalability of our witness and opens the door for distributing photonic multipartite entanglement in quantum networks at high rates.

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[1] H. Jeff Kimble ``The quantum internet'' Nature 453, 1023-1030 (2008).
https:/​/​doi.org/​10.1038/​nature07127

[2] Stephanie Wehner, David Elkouss, and Ronald Hanson, ``Quantum internet: A vision for the road ahead'' Science 362, eaam9288 (2018).
https:/​/​doi.org/​10.1126/​science.aam9288

[3] Peter Kómár, Eric M. Kessler, Michael Bishof, Liang Jiang, Anders S. Sørensen, Jun Ye, and Mikhail D. Lukin, ``A quantum network of clocks'' Nature Physics 10, 582–587 (2014).
https:/​/​doi.org/​10.1038/​nphys3000

[4] Li-Zheng Liu, Yu-Zhe Zhang, Zheng-Da Li, Rui Zhang, Xu-Fei Yin, Yue-Yang Fei, Li Li, Nai-Le Liu, Feihu Xu, Yu-Ao Chen, and Jian-Wei Pan, ``Distributed quantum phase estimation with entangled photons'' Nature Photonics 15, 137–142 (2021).
https:/​/​doi.org/​10.1038/​s41566-020-00718-2

[5] Gláucia Murta, Federico Grasselli, Hermann Kampermann, and Dagmar Bruß, ``Quantum Conference Key Agreement: A Review'' Advanced Quantum Technologies 3, 2000025 (2020).
https:/​/​doi.org/​10.1002/​qute.202000025

[6] Victoria Lipinska, Gláucia Murta, and Stephanie Wehner, ``Anonymous transmission in a noisy quantum network using the W state'' Physical Review A 98, 052320 (2018).
https:/​/​doi.org/​10.1103/​PhysRevA.98.052320

[7] Han-Sen Zhong, Yuan Li, Wei Li, Li-Chao Peng, Zu-En Su, Yi Hu, Yu-Ming He, Xing Ding, W. J. Zhang, Hao Li, Lu Zhang, Z. Wang, L. X. You, Xi-Lin Wang, Xiao Jiang, Li Li, Yu-Ao Chen, Nai-Le Liu, Chao-Yang Lu, and Jian-Wei Pan, ``12-photon entanglement and scalable scattershot boson sampling with optimal entangled-photon pairs from parametric down-conversion'' Physical Review Letters 121, 250505 (2018).
https:/​/​doi.org/​10.1103/​PhysRevLett.121.250505

[8] Daniel F. V. James, Paul G. Kwiat, William J. Munro, and Andrew G. White, ``Measurement of qubits'' Physical Review A 64, 052312 (2001).
https:/​/​doi.org/​10.1103/​PhysRevA.64.052312

[9] Nicolas Sangouard, Christoph Simon, Hugues de Riedmatten, and Nicolas Gisin, ``Quantum repeaters based on atomic ensembles and linear optics'' Reviews of Modern Physics 83, 33–80 (2011).
https:/​/​doi.org/​10.1103/​RevModPhys.83.33

[10] L.-M. Duan, Mikhail D. Lukin, J. Ignacio Cirac, and Peter Zoller, ``Long-distance quantum communication with atomic ensembles and linear optics'' Nature 414, 413–418 (2001).
https:/​/​doi.org/​10.1038/​35106500

[11] Christoph Simon, Hugues de Riedmatten, Mikael Afzelius, Nicolas Sangouard, Hugo Zbinden, and Nicolas Gisin, ``Quantum Repeaters with Photon Pair Sources and Multimode Memories'' Phys. Rev. Lett. 98, 190503 (2007).
https:/​/​doi.org/​10.1103/​PhysRevLett.98.190503

[12] Jiří Minář, Hugues de Riedmatten, Christoph Simon, Hugo Zbinden, and Nicolas Gisin, ``Phase-noise measurements in long-fiber interferometers for quantum-repeater applications'' Phys. Rev. A 77, 052325 (2008).
https:/​/​doi.org/​10.1103/​PhysRevA.77.052325

[13] Chin-Wen Chou, Hugues de Riedmatten, Daniel Felinto, Sergey V. Polyakov, Steven J. Van Enk, and H. Jeff Kimble, ``Measurement-induced entanglement for excitation stored in remote atomic ensembles'' Nature 438, 828–832 (2005).
https:/​/​doi.org/​10.1038/​nature04353

[14] L. Slodička, G. Hétet, N. Röck, P. Schindler, M. Hennrich, and R. Blatt, ``Atom-Atom Entanglement by Single-Photon Detection'' Phys. Rev. Lett. 110, 083603 (2013).
https:/​/​doi.org/​10.1103/​PhysRevLett.110.083603

[15] Aymeric Delteil, Zhe Sun, Wei Bo Gao, Emre Togan, Stefan Faelt, and Ataç Imamoglu, ``Generation of heralded entanglement between distant hole spins'' Nature Physics 12, 218–223 (2016).
https:/​/​doi.org/​10.1038/​nphys3605

[16] Robert Stockill, M. J. Stanley, Lukas Huthmacher, E. Clarke, M. Hugues, A. J. Miller, C. Matthiesen, Claire Le Gall, and Mete Atatüre, ``Phase-Tuned Entangled State Generation between Distant Spin Qubits'' Phys. Rev. Lett. 119, 010503 (2017).
https:/​/​doi.org/​10.1103/​PhysRevLett.119.010503

[17] Peter C. Humphreys, Norbert Kalb, Jaco P. J. Morits, Raymond N. Schouten, Raymond F. L. Vermeulen, Daniel J. Twitchen, Matthew Markham, and Ronald Hanson, ``Deterministic delivery of remote entanglement on a quantum network'' Nature 558, 268–273 (2018).
https:/​/​doi.org/​10.1038/​s41586-018-0200-5

[18] Dario Lago-Rivera, Samuele Grandi, Jelena V. Rakonjac, Alessandro Seri, and Hugues de Riedmatten, ``Telecom-heralded entanglement between multimode solid-state quantum memories'' Nature 594, 37–40 (2021).
https:/​/​doi.org/​10.1038/​s41586-021-03481-8

[19] Patrik Caspar, Ephanielle Verbanis, Enky Oudot, Nicolas Maring, Farid Samara, Misael Caloz, Matthieu Perrenoud, Pavel Sekatski, Anthony Martin, Nicolas Sangouard, Hugo Zbinden, and Robert T. Thew, ``Heralded Distribution of Single-Photon Path Entanglement'' Phys. Rev. Lett. 125, 110506 (2020).
https:/​/​doi.org/​10.1103/​PhysRevLett.125.110506

[20] Yong Yu, Fei Ma, Xi-yu Luo, Bo Jing, Peng-fei Sun, Ren-zhou Fang, Chao-wei Yang, Hui Liu, Ming-Yang Zheng, Xiu-Ping Xie, Wei-Jun Zhang, Li-Xing You, Zhen Wang, Teng-Yun Chen, Qiang Zhang, Xiao-Hui Bao, and Jian-Wei Pan, ``Entanglement of two quantum memories via fibres over dozens of kilometres'' Nature 578, 240–245 (2020).
https:/​/​doi.org/​10.1038/​s41586-020-1976-7

[21] Wolfgang Dür, Guifre Vidal, and J. Ignacio Cirac, ``Three qubits can be entangled in two inequivalent ways'' Physical Review A 62, 062314 (2000).
https:/​/​doi.org/​10.1103/​PhysRevA.62.062314

[22] Daniel Gottesman, Thomas Jennewein, and Sarah Croke, ``Longer-Baseline Telescopes Using Quantum Repeaters'' Physical Review Letters 109, 070503 (2012).
https:/​/​doi.org/​10.1103/​PhysRevLett.109.070503

[23] Emil T. Khabiboulline, Johannes Borregaard, Kristiaan De Greve, and Mikhail D. Lukin, ``Optical Interferometry with Quantum Networks'' Physical Review Letters 123, 070504 (2019).
https:/​/​doi.org/​10.1103/​PhysRevLett.123.070504

[24] Emil T. Khabiboulline, Johannes Borregaard, Kristiaan De Greve, and Mikhail D. Lukin, ``Quantum-assisted telescope arrays'' Physical Review A 100, 022316 (2019).
https:/​/​doi.org/​10.1103/​PhysRevA.100.022316

[25] Olivier Morin, Jean-Daniel Bancal, Melvyn Ho, Pavel Sekatski, Virginia D'Auria, Nicolas Gisin, Julien Laurat, and Nicolas Sangouard, ``Witnessing Trustworthy Single-Photon Entanglement with Local Homodyne Measurements'' Phys. Rev. Lett. 110, 130401 (2013).
https:/​/​doi.org/​10.1103/​PhysRevLett.110.130401

[26] Fernando Monteiro, V. Caprara Vivoli, Thiago Guerreiro, Anthony Martin, Jean-Daniel Bancal, Hugo Zbinden, Robert T. Thew, and Nicolas Sangouard, ``Revealing Genuine Optical-Path Entanglement'' Phys. Rev. Lett. 114, 170504 (2015).
https:/​/​doi.org/​10.1103/​PhysRevLett.114.170504

[27] Scott B. Papp, Kyung Soo Choi, Hui Deng, Pavel Lougovski, S. J. van Enk, and H. Jeff Kimble, ``Characterization of Multipartite Entanglement for One Photon Shared Among Four Optical Modes'' Science 324, 764–768 (2009).
https:/​/​doi.org/​10.1126/​science.1172260

[28] Markus Gräfe, René Heilmann, Armando Perez-Leija, Robert Keil, Felix Dreisow, Matthias Heinrich, Hector Moya-Cessa, Stefan Nolte, Demetrios N. Christodoulides, and Alexander Szameit, ``On-chip generation of high-order single-photon W-states'' Nature Photonics 8, 791–795 (2014).
https:/​/​doi.org/​10.1038/​nphoton.2014.204

[29] Matteo G. A. Paris ``Displacement operator by beam splitter'' Physics Letters A 217, 78–80 (1996).
https:/​/​doi.org/​10.1016/​0375-9601(96)00339-8

[30] Valentina Caprara Vivoli, Pavel Sekatski, Jean-Daniel Bancal, Charles Ci Wen Lim, Anthony Martin, Robert T. Thew, Hugo Zbinden, Nicolas Gisin, and Nicolas Sangouard, ``Comparing different approaches for generating random numbers device-independently using a photon pair source'' New Journal of Physics 17, 023023 (2015).
https:/​/​doi.org/​10.1088/​1367-2630/​17/​2/​023023

[31] Wassily Hoeffding ``Probability Inequalities for Sums of Bounded Random Variables'' Journal of the American Statistical Association 58, 13–30 (1963).
https:/​/​doi.org/​10.1080/​01621459.1963.10500830

[32] Natalia Bruno, Anthony Martin, and Robert T. Thew, ``Generation of tunable wavelength coherent states and heralded single photons for quantum optics applications'' Optics Communications 327, 17–21 (2014).
https:/​/​doi.org/​10.1016/​j.optcom.2014.02.025

[33] Misael Caloz, Matthieu Perrenoud, Claire Autebert, Boris Korzh, Markus Weiss, Christian Schönenberger, Richard J. Warburton, Hugo Zbinden, and Félix Bussières, ``High-detection efficiency and low-timing jitter with amorphous superconducting nanowire single-photon detectors'' Applied Physics Letters 112 (2018).
https:/​/​doi.org/​10.1063/​1.5010102

[34] Peter J. Mosley ``Generation of Heralded Single Photons in Pure Quantum States'' thesis (2007).

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