Abstract
Decoy-state method has been widely employed in the quantum key distribution (QKD), since it can not only solve photon-number-splitting attacks but also substantially improve the QKD performance. In conventional three-intensity decoy-state proposal, one not only needs to randomly modulate light sources to different intensities, but also has to prepare them into different bases, which may cost a lot of random numbers in practical applications. Here, we propose a simple decoy-state scheme with biased basis choices where the decoy pulses are only prepared in X basis. Through this way, it can save cost of random numbers and further simplify the electronic control system. Moreover, we carry out corresponding proof-of-principle demonstration. By incorporating with lower-loss asymmetric Mach–Zehnder interferometers and superconducting single-photon detectors, we can obtain a secret key rate of 1.65 kbps at 201 km and 19.5 bps at 280 km coiled optical fibers, respectively, showing very promising applications in future quantum communications.
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Acknowledgements
The authors gratefully appreciate Hengtong Optic-Electric Co., Ltd., for providing lower-loss fibers. We gratefully acknowledge the financial support from the National Key R&D Program of China (Nos. 2018YFA0306400, 2017YFA0304100), the National Natural Science Foundation of China (Nos. 11774180, 61590932), the Leading-edge technology Program of Jiangsu Natural Science Foundation (BK20192001), and the Postgraduate Research & Practice Innovation Program of Jiangsu Province (SJCX19_0250).
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Appendix
Appendix
In this appendix, we will give the derivation process of Eqs. (1) and (2).
For the WCS, the probability of finding an i-photon state with intensity \(\xi \)\((\xi \in \{ \mu , \nu \})\) is given by: \(P_{\xi }(i) = \frac{\xi ^{i}}{i!}e^{-\xi }\). Then, we have
For any \(i \ge 2\), when \(\mu>\nu >0\), \(\frac{\mu }{\nu }>1\), therefore, the following inequalities hold
The Proof for Eq. (1) of the main text is done.
The gains of signal and decoy states can be written as:
With Eqs. (A3) and (A4), it is easy to get
Considering the conditions in Eq. (A2), we can get the following inequality:
It is easy to reach
The proof for Eq. (2) of the main text is finished.
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Wu, WZ., Zhu, JR., Ji, L. et al. Proof-of-principle demonstration of decoy-state quantum key distribution with biased basis choices. Quantum Inf Process 19, 341 (2020). https://doi.org/10.1007/s11128-020-02852-w
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DOI: https://doi.org/10.1007/s11128-020-02852-w