Within quantum cryptography, the Decoy state quantum key distribution (QKD) protocol is the most widely implemented QKD scheme. Practical QKD systems use multi-photon sources, in contrast to the standard BB84 protocol, making them susceptible to photon number splitting (PNS) attacks. This would significantly limit the secure transmission rate or the maximum channel length in practical QKD systems. In decoy state technique, this fundamental weakness of practical QKD systems is addressed by using multiple intensity levels at the transmitter's source, i.e. qubits are transmitted by Alice using randomly chosen intensity levels (one signal state and several decoy states), resulting in varying photon number statistics throughout the channel. At the end of the transmission Alice announces publicly which intensity level has been used for the transmission of each qubit. A successful PNS attack requires maintaining the bit error rate (BER) at the receiver's end, which can not be accomplished with multiple photon number statistics. By monitoring BERs associated with each intensity level, the two legitimate parties will be able to detect a PNS attack, with highly increased secure transmission rates or maximum channel lengths, making QKD systems suitable for practical applications.

Motivation

In the security proofs of QKD protocols, such as BB84, a single photon source is assumed to be used by the sender, Alice. In reality, a perfect single photon source does not exist. Instead, practical sources, such as weak coherent state laser source, are widely used for QKD. The key problem with these practical QKD sources lies on their multi-photon components. A serious security loophole exists when Alice uses multi-photon states as quantum information carriers. With multi-photon components, an eavesdropper, Eve, could in principle split the photons, keep one photon, and send the rest to Bob. After Alice and Bob announce the basis information, Eve can measure the intercepted photon to get the key information. When the channel is lossy, Eve can launch more sophisticated attacks, such as the photon number splitting attack. In order to minimize the effects of multi-photon states, Alice has to use an extremely weak laser source, which results in a relatively low speed of QKD. The decoy-state method is proposed to solve this multi-photon issue by using a few different photon intensities instead of one. With decoy states, the practical sources, such as a coherent-state source or heralded parametric down-conversion (PDC) source, perform almost as well as a single photon source. [1]

Development

The decoy-state scheme was proposed by Won-Young Hwang from Northwestern University.[2] Later, its security was proven by developing a photon number channel model and assuming the usage of an infinite number of decoy states.[3] A common practical decoy-state method only needs two decoy states, vacuum decoy and weak decoy. This vacuum+weak decoy state method was first proposed by Hoi-Kwong Lo from University of Toronto,[4] and then was analyzed by others. [5][6] It has been shown that with only the vacuum and weak decoy states, the achieved key rate is very close to the infinite decoy state case.[6]

Experimental demonstrations

The first decoy state method experiment was performed by Hoi-Kwong Lo's group and their collaborator Li Qian, [7] where the one-decoy state method [6] is employed. The transmission distance is 15 km and the key generation speed is 165 bit/s. Then, a longer distance QKD is demonstrated with the vacuum+weak decoy state method via 60 km fiber. [8] Later, three experimental groups demonstrate the decoy-state method over 100 km distances. [9][10][11] There are many other demonstrations afterwards. [12][13]

Decoy-state QKD using non-coherent-state sources

Decoy state QKD protocols with non-coherent-state sources have also been analyzed. Passive decoy state protocol, where the decoy states are prepared passively, is proposed as a parametric down-conversion source.[14][15]

See also

References

  1. ↑ Ma, Xiongfeng (2008). Quantum cryptography: from theory to practice (Ph.D.). University of Toronto. arXiv:0808.1385.
  2. ↑ Hwang, Won-Young (1 July 2003). "Quantum Key Distribution with High Loss: Toward Global Secure Communication". Physical Review Letters. 91 (5): 057901. arXiv:quant-ph/0211153. Bibcode:2003PhRvL..91e7901H. doi:10.1103/physrevlett.91.057901. ISSN 0031-9007. PMID 12906634. S2CID 19225674.
  3. ↑ Lo, Hoi-Kwong; Ma, Xiongfeng; Chen, Kai (16 June 2005). "Decoy State Quantum Key Distribution". Physical Review Letters. American Physical Society (APS). 94 (23): 230504. arXiv:quant-ph/0411004. Bibcode:2005PhRvL..94w0504L. doi:10.1103/physrevlett.94.230504. ISSN 0031-9007. PMID 16090452. S2CID 16938588.
  4. ↑ Lo, Hoi-Kwong (2004). Quantum key distribution with vacua or dim pulses as decoy states. Proceedings of 2004 IEEE International Symposium on Information Theory. New York: IEEE Press. p. 137. doi:10.1109/ISIT.2004.1365174. ISBN 0-7803-8280-3.
  5. ↑ Wang, Xiang-Bin (16 June 2005). "Beating the Photon-Number-Splitting Attack in Practical Quantum Cryptography". Physical Review Letters. 94 (23): 230503. arXiv:quant-ph/0410075. Bibcode:2005PhRvL..94w0503W. doi:10.1103/physrevlett.94.230503. ISSN 0031-9007. PMID 16090451. S2CID 2651690.
  6. 1 2 3 Ma, Xiongfeng; Qi, Bing; Zhao, Yi; Lo, Hoi-Kwong (20 July 2005). "Practical decoy state for quantum key distribution". Physical Review A. American Physical Society (APS). 72 (1): 012326. arXiv:quant-ph/0503005. Bibcode:2005PhRvA..72a2326M. doi:10.1103/physreva.72.012326. ISSN 1050-2947. S2CID 836096.
  7. ↑ Zhao, Yi; Qi, Bing; Ma, Xiongfeng; Lo, Hoi-Kwong; Qian, Li (22 February 2006). "Experimental Quantum Key Distribution with Decoy States". Physical Review Letters. American Physical Society (APS). 96 (7): 070502. arXiv:quant-ph/0503192. Bibcode:2006PhRvL..96g0502Z. doi:10.1103/physrevlett.96.070502. ISSN 0031-9007. PMID 16606067. S2CID 2564853.
  8. ↑ Zhao, Yi; Qi, Bing; Ma, Xiongfeng; Lo, Hoi-kwong; Qian, Li (2006). "Simulation and Implementation of Decoy State Quantum Key Distribution over 60km Telecom Fiber". 2006 IEEE International Symposium on Information Theory. IEEE. pp. 2094–2098. arXiv:quant-ph/0601168. doi:10.1109/isit.2006.261920. ISBN 1-4244-0505-X.
  9. ↑ Rosenberg, Danna; Harrington, Jim W.; Rice, Patrick R.; Hiskett, Philip A.; Peterson, Charles G.; Hughes, Richard J.; Lita, Adriana E.; Nam, Sae Woo; Nordholt, Jane E. (5 January 2007). "Long-Distance Decoy-State Quantum Key Distribution in Optical Fiber". Physical Review Letters. American Physical Society (APS). 98 (1): 010503. arXiv:quant-ph/0607186. Bibcode:2007PhRvL..98a0503R. doi:10.1103/physrevlett.98.010503. ISSN 0031-9007. PMID 17358462. S2CID 1082713.
  10. ↑ Schmitt-Manderbach, Tobias; Weier, Henning; Fürst, Martin; Ursin, Rupert; Tiefenbacher, Felix; Scheidl, Thomas; Perdigues, Josep; Sodnik, Zoran; Kurtsiefer, Christian; Rarity, John G.; Zeilinger, Anton; Weinfurter, Harald (5 January 2007). "Experimental Demonstration of Free-Space Decoy-State Quantum Key Distribution over 144 km". Physical Review Letters. American Physical Society (APS). 98 (1): 010504. Bibcode:2007PhRvL..98a0504S. doi:10.1103/physrevlett.98.010504. ISSN 0031-9007. PMID 17358463. S2CID 15102161.
  11. ↑ Peng, Cheng-Zhi; Zhang, Jun; Yang, Dong; Gao, Wei-Bo; Ma, Huai-Xin; Yin, Hao; Zeng, He-Ping; Yang, Tao; Wang, Xiang-Bin; Pan, Jian-Wei (5 January 2007). "Experimental Long-Distance Decoy-State Quantum Key Distribution Based on Polarization Encoding". Physical Review Letters. 98 (1): 010505. arXiv:quant-ph/0607129. Bibcode:2007PhRvL..98a0505P. doi:10.1103/physrevlett.98.010505. ISSN 0031-9007. PMID 17358464. S2CID 45259447.
  12. ↑ Yuan, Z. L.; Sharpe, A. W.; Shields, A. J. (2007). "Unconditionally secure one-way quantum key distribution using decoy pulses". Applied Physics Letters. AIP Publishing. 90 (1): 011118. arXiv:quant-ph/0610015. Bibcode:2007ApPhL..90a1118Y. doi:10.1063/1.2430685. ISSN 0003-6951. S2CID 20424612.
  13. ↑ Shams Mousavi, S. H.; Gallion, P. (24 July 2009). "Decoy-state quantum key distribution using homodyne detection". Physical Review A. American Physical Society (APS). 80 (1): 012327. arXiv:1411.6155. Bibcode:2009PhRvA..80a2327S. doi:10.1103/physreva.80.012327. ISSN 1050-2947. S2CID 119274803.
  14. ↑ Adachi, Yoritoshi; Yamamoto, Takashi; Koashi, Masato; Imoto, Nobuyuki (2 November 2007). "Simple and Efficient Quantum Key Distribution with Parametric Down-Conversion". Physical Review Letters. 99 (18): 180503. arXiv:quant-ph/0610118. Bibcode:2007PhRvL..99r0503A. doi:10.1103/physrevlett.99.180503. ISSN 0031-9007. PMID 17995389. S2CID 38698156.
  15. ↑ Ma, Xiongfeng; Lo, Hoi-Kwong (9 July 2008). "Quantum key distribution with triggering parametric down-conversion sources". New Journal of Physics. 10 (7): 073018. arXiv:0803.2543. Bibcode:2008NJPh...10g3018M. doi:10.1088/1367-2630/10/7/073018. ISSN 1367-2630.
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