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Subcarrier multiplexing multiple-input multiple-output quantum key distribution scheme with orthogonal quantum states

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Abstract

Quantum key distribution (QKD) system is presently being developed for providing high-security transmission in future free-space optical communication links. However, current QKD technique restricts quantum secure communication to a low bit rate. To improve the QKD bit rate, we propose a subcarrier multiplexing multiple-input multiple-output quantum key distribution (SCM-MQKD) scheme with orthogonal quantum states. Specifically, we firstly present SCM-MQKD system model and drive symmetrical SCM-MQKD system into decoherence-free subspaces. We then utilize bipartite Werner and isotropic states to construct multiple parallel single photon with orthogonal quantum states that are invariant for unitary operations. Finally, we derive the density matrix and the capacity of SCM-MQKD system, respectively. Theoretical analysis and numerical results show that the capacity of SCM-MQKD system will increase \({\log _2}(N^2+1)\) times than that of single-photon QKD system.

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References

  1. Ahmad, H.F., Muhammad, D., Pua, C.H., Thambiratnam, K.: Dual-wavelength fiber lasers for the optical generation of microwave and terahertz radiation. IEEE J. Sel. Top. Quantum Electron. 20(5), 0902308-1–0902308-8 (2014)

    Google Scholar 

  2. Capmany, J., Fernandez-Pousa, C.R.: Analysis of subcarrier multiplexed quantum key distribution systems: signal, intermodulation, and quantum bit error rate. IEEE J. Sel. Top. Quantum Electron. 15(6), 1607–1621 (2009)

    Article  Google Scholar 

  3. Capmany, J., Fernandez-Pousa, C.R.: Analysis of passive optical networks for subcarrier multiplexed quantum key distribution. IEEE Trans. Microw. Theory Tech. 58(11), 3220–3228 (2010)

    Article  ADS  Google Scholar 

  4. Mora, J., Ruiz-Alba, A., Amaya, W., Capmany, J.: Multidimensional QKD based on combined orbital and spin angular momenta of photon. IEEE Photon. J. 3(3), 433–440 (2011)

    Article  Google Scholar 

  5. Zueco, D., Mazo, J.J., Solano, E., Garcia-Ripoll, J.J.: Multiplexing scheme for simplified entanglement-based large-alphabet quantum key distribution. Phys. Rev. B 86(2), 024503-1–024503-11 (2012)

    Article  ADS  Google Scholar 

  6. Mazzarella, L., Ticozzi, F., Sergienko, A.V., Vallone, G., Villoresi, P.: Asymmetric architecture for heralded single-photon sources. Phys. Rev. A 88(2), 023848-1–023848-10 (2013)

    Article  ADS  Google Scholar 

  7. Muga, N.J., Ferreira, Mario F.S., Pinto, A.N.: QBER estimation in QKD systems with polarization encoding. J. Lightwave Technol. 29(3), 355–361 (2011)

    Article  ADS  Google Scholar 

  8. Lupo, C., Giovannetti, V., Pirandola, S., Mancini, S., Lloyd, S.: Single-photon interference in sidebands of phase-modulated light for quantum cryptography. Phys. Rev. A 84(1), 010303-1–010303-6 (2011)

    Article  ADS  Google Scholar 

  9. Djordjevic, I.B.: Multidimensional QKD based on combined orbital and spin angular momenta of photon. IEEE Photon. J. 5(6), 7600112-1–7600112-11 (2013)

    Article  Google Scholar 

  10. Hurtado, A., Raghunathan, R., Henning, I.D., Adams, M.J., Lester, L.F.: Simultaneous microwave- and millimeter-wave signal generation with a 1310-nm quantum-dot-distributed feedback laser. IEEE J. Sel. Top. Quantum Electron. 21(6), 1801207-1–1801207-7 (2015)

    Article  Google Scholar 

  11. Dada, A.C.: Multiplexing scheme for simplified entanglement-based large-alphabet quantum key distribution. Phys. Rev. A 91(5), 052313-1–052313-7 (2015)

    Article  ADS  Google Scholar 

  12. Ruiz-Alba, A., Mora, J., Amava, W., Martinez, A., Garcia-Munoz, V., Calvo, D., Capmany, J.: Microwave photonics parallel quantum key distribution. IEEE Photon. J. 4(3), 931–942 (2012)

    Article  Google Scholar 

  13. Zhao, G.H., Zhao, S.H., Yao, Z.S., Meng, W., Wang, X., Zhu, Z., Liu, F.: Forward spectral filtering parallel quantum key distribution system. Opt. Commun. 298–299, 254–259 (2013)

    Article  Google Scholar 

  14. Fang, J., Huang, P., Zeng, G.H.: Multichannel parallel continuous-variable quantum key distribution with Gaussian modulation. Phys. Rev. A 89(2), 022315-1–022315-9 (2014)

    Article  ADS  Google Scholar 

  15. Gabay, M., Amon, S.: Quantum key distribution by a free-space MIMO system. J. Lightwave Technol. 24(8), 3114–3120 (2006)

    Article  ADS  Google Scholar 

  16. Abruzzo, S., Kampermann, H., Bruß, D.: Finite-range multiplexing enhances quantum key distribution via quantum repeaters. Phys. Rev. A 89(1), 012303-1–012303-8 (2014)

    ADS  Google Scholar 

  17. Xiao, H., Ouyang, S.: Capacity of MIMO quantum depolarizing channels. J. Appl. Phys. 112(3), 034903-1–034903-6 (2012)

    Article  ADS  Google Scholar 

  18. Yin, Z.Q., Zhao, Y.B., Zhou, Z.W., Han, Z.F., Guo, G.C.: Decoy states for quantum key distribution based on decoherence-free subspaces. Phys. Rev. A 77(6), 062326-1–062326-6 (2008)

    ADS  Google Scholar 

  19. Zhou, X.P., Su, S.L., Guo, Q., Wang, H.F., Zhu, A.D., Zhang, S.: Parity-gate-based quantum information processing in decoherence-free subspace with nitrogen-vacancy centers. Opt. Commun. 352, 140–147 (2015)

    Article  ADS  Google Scholar 

  20. Shor, P.W.: Scheme for reducing decoherence in quantum computer memory. Phys. Rev. A 52(4), 2493–2496 (1995)

    Article  ADS  Google Scholar 

  21. Ticozzi, F., Viola, L.: Quantum markovian subsystems: invariance, attractivity, and control. IEEE Trans. Autom. Control 53(9), 2048–2063 (2008)

    Article  MathSciNet  Google Scholar 

  22. Brooke, P.G., Cresser, J.D., Patra, M.K.: Decoherence-free quantum information in the presence of dynamical evolution. Phys. Rev. A 77(6), 062313-1–062313-8 (2008)

    Article  ADS  Google Scholar 

  23. Shaham, A., Eisenberg, H.S.: Realizing controllable depolarization in photonic quantum-information channels. Phys. Rev. A 83(2), 022303-1–022303-5 (2011)

    Article  ADS  Google Scholar 

  24. Wang, C.Q., Xu, B.M., Zou, J., He, Z., Yan, Y., Li, J.G., Shao, B.: Feed-forward control for quantum state protection against decoherence. Phys. Rev. A 89(3), 032303-1–032303-11 (2014)

    ADS  Google Scholar 

  25. Zanardi, P., Rasctti, M.: Noisless quantum codes. Phys. Rev. Lett. 79(17), 3306–3309 (1997)

    Article  ADS  Google Scholar 

  26. Chruscinski, D., Kossakowski, A.: Multipartite invariant states. II. Orthogonal symmetry. Phys. Rev. A 73(6), 062315-1–062315-6 (2006)

    ADS  MathSciNet  Google Scholar 

  27. Bennett, C.H., DiVincenzo, D.P., Fuchs, C.A., Mor, T., Rains, E., Shor, P.W., Smolin, J.A.: Quantum nonlocality without entanglement. Phys. Rev. A 59(2), 1070–1091 (1999)

    Article  ADS  MathSciNet  Google Scholar 

  28. Arrigo, A.D., Benenti, G., Falci, G., Macchiavello, C.: Classical and quantum capacities of a fully correlated amplitude damping channel. Phys. Rev. A 88(4), 042337-1–042337-15 (2013)

    Article  ADS  Google Scholar 

  29. Goldenberg, L., Vaidman, L.: Quantum cryptography based on orthogonal states. Phys. Rev. Lett. 75(7), 1239–1243 (1995)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  30. Koashi, M., Imoto, N.: Quantum cryptography based on split transmission of one-bit information in two steps. Phys. Rev. Lett. 79(12), 2383–2386 (1997)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  31. Guo, G.P., Li, C.F., Shi, B.S., Guo, G.C.: Quantum key distribution scheme with orthogonal product states. Phys. Rev. A 64(4), 042301-1–042301-4 (2001)

    Article  ADS  Google Scholar 

  32. Yang, Y.H., Gao, F., Tian, G.J., Cao, T.Q., Wen, Q.Y.: Local distinguishability of orthogonal quantum states in a \(2\times 2\times 2\) system. Phys. Rev. A 88(2), 024301-1–024301-4 (2013)

    ADS  Google Scholar 

  33. Shor, P.W., Preskill, J.: Simple proof of security of the BB84 quantum key distribution protocol. Phys. Rev. Lett. 85(2), 441–444 (2000)

    Article  ADS  Google Scholar 

  34. Capmany, J., Fernandez-Pousa, C.R.: Impact of third-order intermodulation on the performance of subcarrier multiplexed quantum key distribution. J. Lightwave Technol. 29(20), 3061–3069 (2011)

    Article  ADS  Google Scholar 

  35. Fiorentino, M., Wong, F.N.C.: Deterministic controlled-NOT gate for single-photon two-qubit quantum logic. Phys. Rev. Lett. 93(7), 070502-1–070502-4 (2004)

    Article  ADS  Google Scholar 

  36. Silva, R., Guryanova, Y., Brunner, N., Linden, N., Short, A.J., Popescu, S.: Pre- and postselected quantum states: density matrices, tomography, and Kraus operators. Phys. Rev. A 89(1), 012121-1–012121-8 (2014)

    Article  ADS  Google Scholar 

  37. Shapiro, J.H., Wong, F.N.C.: Attacking quantum key distribution with single-photon two-qubit quantum logic. Phys. Rev. A 73(1), 012315-1–012315-7 (2006)

    Article  ADS  Google Scholar 

  38. Duan, L.M., Guo, G.C.: Optimal quantum codes for preventing collective amplitude damping. Phys. Rev. A 58(5), 3491–3495 (1998)

    Article  ADS  Google Scholar 

  39. Kwiat, P.G., Berglund, A.J., Altepeter, J.B., White, A.G.: Experimental verification of decoherence-free subspaces. Science 290, 498–501 (2000)

    Article  ADS  Google Scholar 

  40. Duan, L.M., Guo, G.C.: Preserving coherence in quantum computation by pairing quantum bits. Phys. Rev. Lett. 79(10), 1953–1956 (1997)

    Article  ADS  Google Scholar 

  41. Fan, H., Roychowdhury, V., Szkopek, T.: Optimal two-qubit quantum circuits using exchange interactions. Phys. Rev. A 72, 052323-1–052323-4 (2005)

    Article  ADS  Google Scholar 

  42. Guo, G.P., Li, C.F., Shi, B.S., Li, J., Guo, G.C.: Quantum key distribution scheme with orthogonal product states. Phys. Rev. A 64(4), 042301-1–042301-4 (2001)

    Article  ADS  Google Scholar 

  43. Lo, H.-K., Curty, M., Qi, B.: Measurement-device-independent quantum key distribution. Phys. Rev. Lett. 108, 130503-1–130503-5 (2012)

    Article  ADS  Google Scholar 

  44. Jasim, O.K., Abbas, S., El-Horbaty, E.S.M., Salem, A.B.M.: Quantum key distribution: simulation and characterizations. Proc. Comput. Sci. 65, 701–710 (2015)

    Article  Google Scholar 

  45. Joseph, B., Tulio, Q.M., Nicolas, B.: Certifying the dimension of classical and quantum systems in a prepare-and-measure scenario with independent devices. Phys. Rev. Lett. 112, 140407-1–140407-5 (2014)

    Google Scholar 

  46. Li, H.W., Yin, Z.Q., Wang, S., Guo, G.C., Han, Z.F.: Quantum key distribution based on quantum dimension and independent devices. Phys. Rev. A 89(3), 032302-1–032302-5 (2014)

    ADS  Google Scholar 

  47. Chruscinski, D., Kossakowski, A.: Multipartite invariant states. I. Unitary symmetry. Phys. Rev. A 73(6), 062314-1–062314-10 (2006)

    ADS  MathSciNet  Google Scholar 

  48. Takeoka, M., Guha, S., Wilde, M.M.: Fundamental rate-loss tradeoff for optical quantum key distribution. Nat. Commun. 5, 5235–5242 (2014)

    Article  ADS  Google Scholar 

  49. Chandrasekaran, N., Shapiro, J.H., Wang, L.: Photon information efficient communication through atmospheric turbulencepart II: bounds on ergodic classical and private capacities. J. Lightwave Technol. 32(6), 1088–1097 (2014)

    Article  ADS  Google Scholar 

  50. Holevo, A.S.: The capacity of the quantum channel with general signal states. IEEE Trans. Inf. Theory 44(1), 269–273 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  51. Schumacher, B., Westmoreland, M.D.: Sending classical information via noisy quantum channels. Phys. Rev. A 56(1), 131–138 (1997)

    Article  ADS  Google Scholar 

  52. Yu, N., Duan, R., Ying, M.: Distinguishability of quantum states by positive operator-valued measures with positive partial transpose. IEEE Trans. Inf. Theory 60(4), 2069–2079 (2014)

    Article  MathSciNet  Google Scholar 

  53. Devetak, I.: The private classical capacity and quantum capacity of a quantum channel. IEEE Trans. Inf. Theory 51(1), 44–55 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  54. Renes, J.M., Wilde, M.M.: Polar codes for private and quantum communication over arbitrary channels. IEEE Trans. Inf. Theory 60(6), 3090–3103 (2014)

    Article  MathSciNet  Google Scholar 

  55. Horodecki, K., Horodecki, M., Horodecki, P., Leung, D., Oppenheim, J.: Quantum key distribution based on private states: unconditional security over untrusted channels with zero quantum capacity. IEEE Trans. Inf. Theory 54(6), 2604–2620 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  56. Takeoka, M., Guha, S., Wilde, M.M.: The squashed entanglement of a quantum channel. IEEE Trans. Inf. Theory 60(8), 4987–4998 (2014)

    Article  MathSciNet  Google Scholar 

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Acknowledgements

The authors acknowledge the support from the National Natural Science Foundation of China under Grants 61261018 and 61472094, Guangxi Natural Science Foundation under Grants 2014GXNSFGA118007, and the open research fund of National Mobile Communications Research Laboratory, Southeast University (No. 2015D05).

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Correspondence to Hailin Xiao.

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Xiao, H., Zhang, Z. Subcarrier multiplexing multiple-input multiple-output quantum key distribution scheme with orthogonal quantum states. Quantum Inf Process 16, 13 (2017). https://doi.org/10.1007/s11128-016-1474-x

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