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SCIENCE CHINA Information Sciences, Volume 61, Issue 6: 062501(2018) https://doi.org/10.1007/s11432-017-9291-6

High-rate and high-capacity measurement-device-independent quantum key distribution with Fibonacci matrix coding in free space

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  • ReceivedJun 5, 2017
  • AcceptedOct 26, 2017
  • PublishedMay 7, 2018

Abstract

This paper proposes a high-rate and high-capacitymeasurement-device-independent quantum key distribution (MDI-QKD)protocol with Fibonacci-valued and Lucas-valued orbital angularmomentum (OAM) entangled states in free space. In the existingMDI-OAM-QKD protocols, the main encoding algorithm handles encodednumbers in a bit-by-bit manner. To design a fast encoding algorithm,we introduce a Fibonacci matrix coding algorithm, by which, encodednumbers are separated into segments longer than one bit. By doingso, when compared to the existing MDI-OAM-QKD protocols, the newprotocol can effectively increase the key rate and the codingcapacity. This is because Fibonacci sequences are used in preparingOAM entangled states, reducing the misattribution errors (which slowdown the execution cycle of the entire QKD) in QKD protocols.Moreover, our protocol keeps the data blocks as small as possible,so as to have more blocks in a given time interval. Mostimportantly, our proposed protocol can distill multiple Fibonaccikey matrices from the same block of data, thus reducing thestatistical fluctuations in the sample and increasing the final QKDrate. Last but not the least, the sender and the receiver can omitclassical information exchange and bit flipping in the secure keydistillation stage.


Acknowledgment

Hong LAI was supported by National Natural Science Foundation of China (Grant No. 61702427), Doctoral Program of Higher Education (Grant No. SWU115091), and financial support in part by 1000-Plan of Chongqing by Southwest University (Grant No. SWU116007). Mingxing LUO was supported by National Natural Science Foundation of China (Grant No. 61772437) and Sichuan Youth Science Technique Foundation (Grant No. 2017JQ0048). Jun ZHANG was supported by National Natural Science Foundation of China (Grant No. 61401371). Josef PIEPRZYK has been supported by National Science Centre, Poland (Grant No. UMO-2014/15/B/ST6/05130).


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  • Figure 1

    (Color online) The experimental setup of the proposed OAM-MDI-QKD protocol based on a Vogel spiral. The laser sources in Alice's and Bob's labs pump Barium borate (BBO) crystals to prepare Fibonacci- and Lucas-valued pairs of entangled photons with the spontaneous parametric down conversion (SPDC). The crystal planes are imaged onto the spatial light modulators (SLMs), and every SLM is imaged onto the input of a single-mode fiber (SMF). Then single photons are detected with detectors $L_{A},L_{B},L_{C_1}\!,L_{C_2}\!,D_{C_1}\!,D_{C_{2}}$ in Alice's, Bob's and Charlie's laboratories. The detectors $L_{A}, L_{B},L_{C_{1}}\!,L_{C_{2}}$ are used only for letting Fibonacci-valued photons reach the arrays of single-photon detectors, while the OAM-sorters R1 and R2 (two static optical elements) and a lens (L) are used for differentiating the superpositions of the form $\frac{1}{\sqrt{2}}(|F_{k-2}\rangle+|F_{k}\rangle)$ and $\frac{1}{\sqrt{2}}(|F_{k-1}\rangle+|L_{k}\rangle)$ respectively, and blocking any non-Fibonacci values. $D_{C_{1}}\!,D_{C_{2}}$ can be used to detect the superposition states $\frac{1}{\sqrt{2}}(|F_{k-2}\rangle+|F_{k}\rangle)$ and $\frac{1}{\sqrt{2}}(|F_{k-1}\rangle+|L_{k}\rangle)$ respectively. BS denotes beam splitter with $50:50$.

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