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Experimental few-copy multipartite entanglement detection

Abstract

Many future quantum technologies rely on the generation of entangled states. Quantum devices will require verification of their operation below some error threshold, but the reliable detection of quantum entanglement remains a considerable challenge for large-scale quantum systems. Well-established techniques for this task rely on the measurement of expectation values of entanglement witnesses; however these require many measurement settings to be extracted. Here, we develop a generic framework for efficient entanglement detection that translates any entanglement witness into a resource-efficient probabilistic scheme, whose confidence grows exponentially with the number of individual detection events, namely copies of the quantum state. To benchmark our findings, we experimentally verify the presence of entanglement in a photonic six-qubit cluster state generated using three single-photon sources operating at telecommunication wavelengths. We find that the presence of entanglement can be certified with at least 99.74% confidence by detecting 20 copies of the quantum state. Additionally, we show that genuine six-qubit entanglement is verified with at least 99% confidence by using 112 copies of the state. Our protocol can be carried out with a remarkably low number of copies and in the presence of experimental imperfections, making it a practical and applicable method to verify large-scale quantum devices.

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Data availability

The data that support the plots within this paper and other findings of this study are available from the corresponding author on reasonable request.

References

  1. 1.

    Arrazola, J. M. et al. Reliable entanglement verification. Phys. Rev. A 87, 062331 (2013).

  2. 2.

    Wang, X.-L. et al. Experimental ten-photon entanglement. Phys. Rev. Lett. 117, 210502 (2016).

  3. 3.

    Monz, T. et al. 14-qubit entanglement: creation and coherence. Phys. Rev. Lett. 106, 130506 (2011).

  4. 4.

    Song, C. et al. 10-qubit entanglement and parallel logic operations with a superconducting circuit. Phys. Rev. Lett. 119, 180511 (2017).

  5. 5.

    Friis, N. et al. Observation of entangled states of a fully controlled 20-qubit system. Phys. Rev. X 8, 021012 (2018).

  6. 6.

    Wang, X.-L. et al. 18-qubit entanglement with six photons’ three degrees of freedom. Phys. Rev. Lett. 120, 260502 (2018).

  7. 7.

    Chen, M., Menicucci, N. C. & Pfister, O. Experimental realization of multipartite entanglement of 60 modes of a quantum optical frequency comb. Phys. Rev. Lett. 112, 120505 (2014).

  8. 8.

    Yoshikawa, J.-I. et al. Generation of one-million-mode continuous-variable cluster state by unlimited time-domain multiplexing. APL Photon. 1, 060801 (2016).

  9. 9.

    Cai, Y. et al. Multimode entanglement in reconfigurable graph states using optical frequency combs. Nat. Commun. 8, 15645–15653 (2017).

  10. 10.

    James, D. F. V., Kwiat, P. G., Munro, W. J. & White, A. G. Measurement of qubits. Phys. Rev. A 64, 052312 (2001).

  11. 11.

    Gühne, O. & Tóth, G. Entanglement detection. Phys. Rep. 474, 1–75 (2009).

  12. 12.

    Tóth, G. & Gühne, O. Detecting genuine multipartite entanglement with two local measurements. Phys. Rev. Lett. 94, 060501 (2005).

  13. 13.

    Knips, L., Schwemmer, C., Klein, N., Wieśniak, M. & Weinfurter, H. Multipartite entanglement detection with minimal effort. Phys. Rev. Lett. 117, 210504 (2016).

  14. 14.

    Tran, M. C., Dakić, B., Arnault, F., Laskowski, W. & Paterek, T. Quantum entanglement from random measurements. Phys. Rev. A 92, 050301 (2015).

  15. 15.

    Bavaresco, J. et al. Measurements in two bases are sufficient for certifying high-dimensional entanglement. Nat. Phys. 14, 1032–1037 (2018).

  16. 16.

    Knill, E. et al. Randomized benchmarking of quantum gates. Phys. Rev. A 77, 012307 (2008).

  17. 17.

    Gross, D., Liu, Y.-K., Flammia, S. T., Becker, S. & Eisert, J. Quantum state tomography via compressed sensing. Phys. Rev. Lett. 105, 150401 (2010).

  18. 18.

    Montanaro, A. Learning stabilizer states by Bell sampling. Preprint at https://arXiv.org/abs/1707.04012 (2017).

  19. 19.

    Torlai, G. et al. Neural-network quantum state tomography. Nat. Phys. 14, 447–450 (2018).

  20. 20.

    Flammia, S. T. & Liu, Y.-K. Direct fidelity estimation from few Pauli measurements. Phys. Rev. Lett. 106, 230501 (2011).

  21. 21.

    Mayers, D. & Yao, A. Self testing quantum apparatus. QIC 4, 273–286 (2004).

  22. 22.

    McKague, M. in Theory of Quantum Computation, Communication, and Cryptography Vol. 6745 (eds Bacon, D., Martin-Delgado, M. & Roettler, M) 104–120 (Springer, 2014).

  23. 23.

    Bancal, J.-D., Navascués, M., Scarani, V., Vértesi, T. & Yang, T. H. Physical characterization of quantum devices from nonlocal correlations. Phys. Rev. A 91, 022115 (2015).

  24. 24.

    Miller, C. A. & Shi, Y. Optimal robust quantum self-testing by binary nonlocal XOR games. Preprint at https://arXiv.org/abs/1207.1819 (2012).

  25. 25.

    Reichardt, B. W., Unger, F. & Vazirani, U. A classical leash for a quantum system: command of quantum systems via rigidity of CHSH games. Preprint at https://arXiv.org/abs/1209.0448 (2012).

  26. 26.

    McKague, M., Yang, T. H. & Scarani, V. Robust self-testing of the singlet. J. Phys. A Math. Theor. 45, 455304 (2012).

  27. 27.

    Takeuchi, Y. & Morimae, T. Verification of many-qubit states. Phys. Rev. X 8, 021060 (2018).

  28. 28.

    Zhu, H. & Hayashi, M. Efficient verification of hypergraph states. Preprint at https://arXiv.org/abs/1806.05565 (2018).

  29. 29.

    Pappa, A., Chailloux, A., Wehner, S., Diamanti, E. & Kerenidis, I. Multipartite entanglement verification resistant against dishonest parties. Phys. Rev. Lett. 108, 260502 (2012).

  30. 30.

    McCutcheon, W. et al. Experimental verification of multipartite entanglement in quantum networks. Nat. Commun. 7, 13251–13258 (2016).

  31. 31.

    Pallister, S., Linden, N. & Montanaro, A. Optimal verification of entangled states with local measurements. Phys. Rev. Lett. 120, 170502 (2018).

  32. 32.

    Schneeloch, J., Tison, C. C., Fanto, M. L., Alsing, P. M. & Howland, G. A. Quantifying entanglement in a 68-billion dimensional quantum systems. Preprint at https://arXiv.org/abs/1804.04515 (2018).

  33. 33.

    Barreiro, J. T. et al. Demonstration of genuine multipartite entanglement with device-independent witnesses. Nat. Phys. 9, 559–562 (2013).

  34. 34.

    Dimić, A. & Dakić, B. Single-copy entanglement detection. npj Quantum Inf. 4, 11–18 (2018).

  35. 35.

    Jungnitsch, B. et al. Increasing the statistical significance of entanglement detection in experiments. Phys. Rev. Lett. 104, 210401 (2010).

  36. 36.

    Blume-Kohout, R. Robust error bars for quantum tomography. Preprint at https://arXiv.org/abs/1202.5270 (2012).

  37. 37.

    Lu, C.-Y. et al. Experimental entanglement of six photons in graph states. Nat. Phys. 3, 91–95 (2007).

  38. 38.

    Hein, M., Eisert, J. & Briegel, H. J. Multiparty entanglement in graph states. Phys. Rev. A 69, 062311 (2004).

  39. 39.

    Gerke, S., Vogel, W. & Sperling, J. Numerical construction of multipartite entanglement witnesses. Phys. Rev. X 8, 031047 (2018).

  40. 40.

    Greganti, C. et al. Tuning single-photon sources for telecom multi-photon experiments. Opt. Express 26, 3286–3302 (2018).

  41. 41.

    Broome, M. A., Almeida, M. P., Fedrizzi, A. & White, A. G. Reducing multi-photon rates in pulsed down-conversion by temporal multiplexing. Opt. Express 19, 22698–22708 (2011).

  42. 42.

    Kim, T., Fiorentino, M. & Wong, F. N. C. Phase-stable source of polarization-entangled photons using a polarization Sagnac interferometer. Phys. Rev. A 73, 012316 (2006).

  43. 43.

    Fedrizzi, A., Herbst, T., Poppe, A., Jennewein, T. & Zeilinger, A. A wavelength-tunable fiber-coupled source of narrowband entangled photons. Opt. Express 15, 15377–15386 (2007).

  44. 44.

    Kuzucu, O. & Wong, F. N. Pulsed Sagnac source of narrow-band polarization-entangled photons. Phys. Rev. A 77, 032314 (2008).

  45. 45.

    Jin, R.-B. et al. Pulsed Sagnac polarization-entangled photon source with a PPKTP crystal at telecom wavelength. Opt. Express 22, 11498–11507 (2014).

  46. 46.

    Natarajan, C. M., Tanner, M. G. & Hadfield, R. H. Superconducting nanowire single-photon detectors: physics and applications. Supercond. Sci. Technol. 25, 063001–063016 (2012).

  47. 47.

    Marsili, F. et al. Detecting single infrared photons with 93% system efficiency. Nat. Photon. 7, 210–214 (2013).

  48. 48.

    Tóth, G. Entanglement witnesses in spin models. Phys. Rev. A 71, 010301 (2005).

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Acknowledgements

The authors thank I. Alonso Calafell for help with the detectors and T. Strömberg for helpful discussions. V.S. acknowledges support from the University of Vienna through the Vienna Doctoral School. A.D. acknowledges support from project no. ON171035 of the Serbian Ministry of Education and Science and from the scholarship awarded from The Austrian Agency for International Cooperation in Education and Research (OeAD-GmbH). L.A.R. acknowledges support from the Templeton World Charity Foundation (fellowship no. TWCF0194). P.W. acknowledges support from the European Commission through ErBeStA (no. 800942), from the Austrian Science Fund (FWF) through CoQuS (W1210-N25), BeyondC (F7113-N38) and NaMuG (P30067-N36), the US Air Force Office of Scientific Research (FA2386-232 17-1-4011), the Austrian Research Promotion Agency (FFG) through the QuantERA ERA-NET Cofund project HiPhoP, and Red Bull. B.D. acknowledges support from the Foundational Question Institute (FQXi) grant FQXi-MGA-1806 and from an ESQ Discovery Grant of the Austrian Academy of Sciences.

Author information

V.S., C.G. and P.W. designed the experiment. V.S. and C.G. built the set-up. V.S. performed data analysis. L.A.R. worked on the detectors. A.D. and B.D. developed the theoretical idea. L.A.R., P.W. and B.D. supervised the project. All authors contributed to writing the paper.

Correspondence to Valeria Saggio.

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Fig. 1: Illustration of the entanglement detection protocol.
Fig. 2: Schematic of an H-shaped six-qubit cluster state.
Fig. 3: Experimental set-up.
Fig. 4: Growth of confidence of entanglement with the number of copies of the quantum state.