# Implementation of quantum key distribution surpassing the linear rate-transmittance bound

## Abstract

Quantum key distribution (QKD)1,2 offers a long-term solution to secure key exchange. Due to photon loss in transmission, it was believed that the repeaterless key rate is bounded by a linear function of the transmittance, O(η) (refs. 3,4), limiting the maximal secure transmission distance5,6. Recently, a novel type of QKD scheme has been shown to beat the linear bound and achieve a key rate performance of $$O(\sqrt{\eta })$$ (refs. 7,8,9). Here, by employing the laser injection technique and the phase post-compensation method, we match the modes of two independent lasers and overcome the phase fluctuation. As a result, the key rate surpasses the linear bound via 302 km and 402 km commercial-fibre channels, over four orders of magnitude higher than existing results5. Furthermore, our system yields a secret key rate of 0.118 bps with a 502 km ultralow-loss fibre. This new type of QKD pushes forward long-distance quantum communication for the future quantum internet.

## Access options

from\$8.99

All prices are NET prices.

## Data availability

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

## References

1. 1.

Bennett, C. H. & Brassard, G. Quantum cryptography: public key distribution and coin tossing. In Proc. IEEE International Conference on Computers, Systems and Signal Processing 175–179 (IEEE, 1984).

2. 2.

Ekert, A. K. Quantum cryptography based on Bell’s theorem. Phys. Rev. Lett. 67, 661–663 (1991).

3. 3.

Takeoka, M., Guha, S. & Wilde, M. M. Fundamental rate-loss tradeoff for optical quantum key distribution. Nat. Commun. 5, 5235 (2014).

4. 4.

Pirandola, S., Laurenza, R., Ottaviani, C. & Banchi, L. Fundamental limits of repeaterless quantum communications. Nat. Commun. 8, 15043 (2017).

5. 5.

Yin, H.-L. et al. Measurement-device-independent quantum key distribution over a 404 km optical fiber. Phys. Rev. Lett. 117, 190501 (2016).

6. 6.

Boaron, A. et al. Secure quantum key distribution over 421 km of optical fiber. Phys. Rev. Lett. 121, 190502 (2018).

7. 7.

Lucamarini, M., Yuan, Z., Dynes, J. & Shields, A. Overcoming the rate–distance limit of quantum key distribution without quantum repeaters. Nature 557, 400–403 (2018).

8. 8.

Ma, X., Zeng, P. & Zhou, H. Phase-matching quantum key distribution. Phys. Rev. X 8, 031043 (2018).

9. 9.

Lin, J. & Lütkenhaus, N. Simple security analysis of phase-matching measurement-device-independent quantum key distribution. Phys. Rev. A 98, 042332 (2018).

10. 10.

Lo, H.-K., Curty, M. & Qi, B. Measurement-device-independent quantum key distribution. Phys. Rev. Lett. 108, 130503 (2012).

11. 11.

Hwang, W.-Y. Quantum key distribution with high loss: toward global secure communication. Phys. Rev. Lett. 91, 057901 (2003).

12. 12.

Lo, H.-K., Ma, X. & Chen, K. Decoy state quantum key distribution. Phys. Rev. Lett. 94, 230504 (2005).

13. 13.

Wang, X.-B. Beating the photon-number-splitting attack in practical quantum cryptography. Phys. Rev. Lett. 94, 230503 (2005).

14. 14.

Minder, M. et al. Experimental quantum key distribution beyond the repeaterless secret key capacity. Nat. Photon. 13, 334–338 (2019).

15. 15.

Liu, Y. et al. Experimental twin-field quantum key distribution through sending or not sending. Phys. Rev. Lett. 123, 100505 (2019).

16. 16.

Wang, S. et al. Beating the fundamental rate-distance limit in a proof-of-principle quantum key distribution system. Phys. Rev. X 9, 021046 (2019).

17. 17.

Zhong, X., Hu, J., Curty, M., Qian, L. & Lo, H.-K. Proof-of-principle experimental demonstration of twin-field type quantum key distribution. Phys. Rev. Lett. 123, 100506 (2019).

18. 18.

Yuan, Z. et al. Directly phase-modulated light source. Phys. Rev. X 6, 031044 (2016).

19. 19.

Comandar, L. et al. Quantum key distribution without detector vulnerabilities using optically seeded lasers. Nat. Photon. 10, 312–315 (2016).

20. 20.

Lipka, M., Parniak, M. & Wasilewski, W. Optical frequency locked loop for long-term stabilization of broad-line DFB laser frequency difference. Appl. Phys. B 123, 238 (2017).

21. 21.

Ma, X. & Razavi, M. Alternative schemes for measurement-device-independent quantum key distribution. Phys. Rev. A 86, 062319 (2012).

22. 22.

Zeng, P., Wu, W. & Ma, X. Symmetry-protected privacy: beating the rate–distance linear bound over a noisy channel. Preprint at https://arxiv.org/abs/1910.05737 (2019).

23. 23.

Zukowski, M., Zeilinger, A., Horne, M. A. & Ekert, A. K. Event-ready-detectors Bell experiment via entanglement swapping. Phys. Rev. Lett. 71, 4287–4290 (1993).

24. 24.

Briegel, H.-J., Dür, W., Cirac, J. I. & Zoller, P. Quantum repeaters: the role of imperfect local operations in quantum communication. Phys. Rev. Lett. 81, 5932–5935 (1998).

## Acknowledgements

We thank H. Zhou for insightful discussions. This work was supported by the National Key R&D Program of China (2017YFA0303903), the Chinese Academy of Science, the National Fundamental Research Program, the National Natural Science Foundation of China (grants 11875173, 61875182 and 11674193) and Anhui Initiative in Quantum Information Technologies and Fundamental Research Funds for the Central Universities (WK2340000083).

## Author information

X.M., T.-Y.C. and J.-W.P. conceived the research. Y.-A.C. Q.Z., C.-Z.P., X.M., T.-Y.C. and J.-W.P. designed the experiment. X.-T.F., H.Liu and T.-Y.C. carried out the experiment. P.Z., W.W. and X.M. performed the protocol security analysis and data post-processing. M.Z. and Y.-L.T. assisted with the experiment scheme discussion and verification. Y.-J.S. designed and developed the voltage pulse generator. Y.X. programmed the field-programmable gate array logic. W.Z., H.Li, Z.W. and L.Y. designed and fabricated the superconducting nanowire single-photon detector. M.-J.L. and H.C. provided the ultralow-loss fibres. P.Z., X.-T.F., H.Liu, X.M., T.-Y.C. and J.-W.P. co-wrote the manuscript, with input from the other authors. All authors discussed the results and proofread the manuscript.

Correspondence to Xiongfeng Ma or Teng-Yun Chen or Jian-Wei Pan.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

## Supplementary information

### Supplementary Information

Supplementary Figs. 1–4, discussion, equations 1–28 and Tables 1–10.

## Rights and permissions

Reprints and Permissions