Source-linked AI summary
Experimental measurement-device-independent quantum key distribution
Yang Liu, Teng-Yun Chen, Liu-Jun Wang, Hao Liang, Guo-Liang Shentu, Jian Wang, Ke Cui, Hua-Lei Yin, Nai-Le Liu, Li Li, Xiongfeng Ma, Jason S. Pelc, M. M. Fejer, Qiang Zhang, Jian-Wei Pan
TL;DR
The paper addresses estimating key-rate parameters for signal and decoy states under assumptions about photon-state quantities. It uses decoy-state estimation and linear programming, while noting that some higher-order-term effects remain for future study.
Problem
Estimating the single-photon yield and phase-error rate is needed to determine the key rate from signal and decoy-state data.
Method
The method estimates Y11 and e11 using decoy states and solves the resulting bounds or minimization problem by linear programming.
Results
The numerical evaluation examined the effect of terms with i, j ≥7 in the parameter-estimation expression.
Takeaways & Limitations
The data-processing procedure can estimate key-rate parameters from decoy-state constraints and use them to calculate the key rate.
Abstract
from arXiv · showhide
Throughout history, every advance in encryption has been defeated by advances in hacking with severe consequences. Quantum cryptography holds the promise to end this battle by offering unconditional security when ideal single-photon sources and detectors are employed. Unfortunately, ideal devices never exist in practice and device imperfections have become the targets of various attacks. By developing up-conversion single-photon detectors with high efficiency and low noise, we build up a measurement-device-independent quantum key distribution (MDI-QKD) system, which is immune to all hacking strategies on detection. Meanwhile, we employ the decoy-state method to defeat attacks on non-ideal source. By closing the loopholes in both source and detection, our practical system, which generates more than 25 kbit secure key over a 50-km fiber link, provides an ultimate solution for communication security.
Appendix A: Key rate
The key-rate post-processing combines signal and decoy detection events, using measured gains and QBERs while estimating single-photon phase errors from decoy-state data. Secure keys can be extracted from any signal or decoy contribution that is positive.
- Secure keys are extracted from all signal and decoy states whose contribution is positive.
- Four intensities on each arm produce 16 signal–decoy combinations for the overall key-rate calculation.
- The key-rate terms use overall gain and QBER for Alice’s and Bob’s intensity choices, together with an error-correction cost determined by the binary Shannon entropy.
- The single-photon phase error rate e11 is assumed to be identical across signal and decoy cases.
- The final key is generated from Z-basis data, while the unmeasurable Z-basis phase error rate is inferred from X-basis bit errors estimated with decoy states.
Appendix B: Parameter estimation by decoy states
Decoy-state parameter estimation uses weak coherent states at multiple intensities to estimate the single-photon yield Y11 and phase error rate e11 needed for privacy amplification. The procedure formulates measurable constraints and solves bounds with linear programming, including statistical fluctuations.
- The privacy-amplification term depends on the two estimated variables Y11 and e11.
- Four coherent-state intensities are used by both Alice and Bob, yielding 16 constraint linear equations for parameter estimation.
- Measured experimental quantities form the left side of the constraints, while the right side contains linear functions of unknown yields and error rates.
- Linear programming computes a lower bound for Y11 and an upper bound for e11 to minimize the privacy-amplification term.
- Terms with i, j ≥7 have negligible effects on parameter estimation and can be discarded to solve the optimization efficiently.
- Directly optimizing the privacy-amplification expression instead of separately bounding Y11 and e11 is left for future study.
- The method incorporates statistical fluctuations by converting equality constraints into inequalities and using three standard deviations in post-processing.