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Fault tolerant quantum secret sharing against collective-amplitude-damping noise

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Abstract

We present a quantum secret sharing protocol against collective-amplitude-damping noise. Each logical qubit is encoded in two qubit noiseless states. So it can function over such a noisy channel. The two agents encode their messages on each logical qubit only by performing a permutation operation on two physical qubits. Although each logical qubit received by each agent only carries a bit of information, the boss Alice can read out her agents’ information by discriminating two orthogonal states by performing single-qubit measurements assisted by local operation and classical communication (LOCC).

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References

  1. Hillery M, Bužek V, Berthiaume A. Quantum secret sharing. Phys Rev A, 1999, 59: 1829–1834

    Article  MathSciNet  ADS  Google Scholar 

  2. Karlsson A, Koashi M, Imoto N. Quantum entanglement for secret sharing and secret splitting. Phys Rev A, 1999, 59: 162–168

    Article  ADS  Google Scholar 

  3. Cleve R, Gottesman D, Lo H K. How to share a quantum secret. Phys Rev Lett, 1999, 83: 648–651

    Article  ADS  Google Scholar 

  4. Xiao L, Long G L, Deng F G, et al. Efficient multiparty quantum secret sharing schemes. Phys Rev A, 2004, 69: 052307

    Article  ADS  Google Scholar 

  5. Gottesman D. Theory of quantum secret sharing. Phys Rev A, 2000, 61: 042311

    Article  MathSciNet  ADS  Google Scholar 

  6. Karimipour V, Bahraminasab A, Bagherinezhad S. Entanglement swapping of generalized cat states and secret sharing. Phys Rev A, 2002, 65: 042320

    Article  ADS  Google Scholar 

  7. Tittel W, Zbinden H, Gisin N. Experimental demonstration of quantum secret sharing. Phys Rev A, 2001, 63: 042301

    Article  ADS  Google Scholar 

  8. Bandyopadhyay S. Teleportation and secret sharing with pure entangled states. Phys Rev A, 2000, 62: 012308

    Article  MathSciNet  ADS  Google Scholar 

  9. Guo G P, Guo G C. Quantum secret sharing without entanglement. Phys Lett A, 2003, 310: 247–251

    Article  MathSciNet  ADS  MATH  Google Scholar 

  10. Chau H F. Practical scheme to share a secret key through a quantum channel with a 27.6% bit error rate. Phys Rev A, 2002, 66: 060302

    Article  ADS  Google Scholar 

  11. Hsu L Y, Li C M. Quantum secret sharing using product states. Phys Rev A, 2005, 71: 022321

    Article  ADS  Google Scholar 

  12. Lance A M, Symul T, Bowen W P, et al. Tripartite quantum state sharing. Phys Rev Lett, 2004, 92: 177903

    Article  ADS  Google Scholar 

  13. Zhang Z J, Li Y, Man Z X. Multiparty quantum secret sharing. Phys Rev A, 2005, 71: 044301

    Article  MathSciNet  ADS  Google Scholar 

  14. Deng F G, Li X H, Li C Y, et al. Multiparty quantum-state sharing of an arbitrary two-particle state with Einstein-Podolsky-Rosen pairs. Phys Rev A, 2005, 72: 044301

    Article  ADS  Google Scholar 

  15. Deng F G, Zhou H Y, Long G L. Bidirectional quantum secret sharing and secret splitting with polarized single photons. Phys Lett A, 2005, 337: 329–334

    Article  ADS  MATH  Google Scholar 

  16. Deng F G, Zhou H Y, Long G L. Circular quantum secret sharing. J Phys A: Math Gen, 2006, 39: 14089–14099

    Article  MathSciNet  ADS  MATH  Google Scholar 

  17. Yan F L, Gao T. Quantum secret sharing between multiparty and multiparty without entanglement. Phys Rev A, 2005, 72: 012304

    Article  ADS  Google Scholar 

  18. Zhang Z J. Multiparty quantum secret sharing of secure direct communication. Phys Lett A, 2005, 342: 60–66

    Article  ADS  MATH  Google Scholar 

  19. Deng F G, Zhou P, Li X H, et al. Efficient multiparty quantum secret sharing with Greenberger-Horne-Zeilinger states. Chin Phys Lett, 2006, 23: 1084–1087

    Article  ADS  Google Scholar 

  20. Zhang Z J, Gao G, Wang X, et al. Multiparty quantum secret sharing based on the improved Bostrom-Felbinger protocol. Opt Commun, 2007, 269: 418–422

    Article  ADS  Google Scholar 

  21. Deng F G, Zhou H Y, Long G L. Bidirectional quantum secret sharing and secret splitting with polarized single photons. Phys Lett A, 2005, 337: 329–334

    Article  ADS  MATH  Google Scholar 

  22. Markham D, Sanders B C. Graph states for quantum secret sharing. Phys Rev A, 2008, 78: 042309

    Article  MathSciNet  ADS  Google Scholar 

  23. Yang Y G, Wen Q Y. Circular threshold quantum secret sharing. Chin Phys B, 2008, 17: 419–423

    Article  ADS  Google Scholar 

  24. Yang Y G, Wen Q Y. Threshold quantum secret sharing between multi-party and multi-party. Sci China Ser G-Phys Mech Astron, 2008, 51: 1308–1315

    Article  ADS  MATH  Google Scholar 

  25. Yang Y G, Wen Q Y. Threshold multiparty quantum-information splitting via quantum channel encryption. Int J Quantum Inform, 2009, 7: 1249–1254

    Article  MATH  Google Scholar 

  26. Wang Y H, Song H S. Preparation of multi-atom specially entangled W-class state and splitting quantum information. Chin Sci Bull, 2009, 54: 2599–2605

    Article  Google Scholar 

  27. Gao T, Yan F L, Li Y C. Quantum secret sharing between m-party and n-party with six states. Sci China Ser G-Phys Mech Astron, 2009, 52: 1191–1202

    Article  ADS  Google Scholar 

  28. Shi R H, Huang L S, Yang W, et al. Quantum secret sharing between multiparty and multiparty with Bell states and Bell measurements. Sci China Ser G-Phys Mech Astron, 2010, 53: 2238–2244

    Article  ADS  Google Scholar 

  29. Hao L, Li J L, Long G L. Eavesdropping in a quantum secret sharing protocol based on Grover algorithm and its solution. Sci China Ser G-Phys Mech Astron, 2010, 53: 491–495

    Article  ADS  Google Scholar 

  30. Nielsen M A, Chuang I L. Quantum Computation and Quantum Information. Cambridge: Cambridge University Press, 2000

    MATH  Google Scholar 

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

    Article  ADS  Google Scholar 

  32. Kalamidas D. Single-photon quantum error rejection and correction with linear optics. Phys Lett A, 2005, 343: 331–335

    Article  ADS  MATH  Google Scholar 

  33. de Brito D B, Ramos R V. Passive quantum error correction with linear optics. Phys Lett A, 2006, 352: 206–209

    Article  ADS  MATH  Google Scholar 

  34. Yamamoto T, Shimamura J, Ozdemir S K Ä, et al. Faithful qubit distribution assisted by one additional qubit against collective noise. Phys Rev Lett, 2005, 95: 040503

    Article  ADS  Google Scholar 

  35. Chen Y A, Zhang A N, Zhao Z, et al. Experimental quantum error rejection for quantum communication. Phys Rev Lett, 2006, 96: 220504

    Article  MathSciNet  ADS  Google Scholar 

  36. Li X H, Deng F G, Zhou H Y. Faithful qubit transmission against collective noise without ancillary qubits. Appl Phys Lett, 2007, 91: 144101

    Article  ADS  Google Scholar 

  37. Walton Z D, Abouraddy A F, Sergienko A V, et al. Decoherence-free subspaces in quantum key distribution. Phys Rev Lett, 2003, 91: 087901

    Article  ADS  Google Scholar 

  38. Boileau J C, Gottesman D, Laflamme R, et al. Robust polarization-based quantum key distribution over a collective-noise channel. Phys Rev Lett, 2004, 92: 017901

    Article  ADS  Google Scholar 

  39. Yamamoto T, Hayashi K, Ozdemir S K, et al. Robust photonic entanglement distribution by state-independent encoding onto decoherence-free subspace. Nat Photonics, 2008, 2: 488–491

    Article  Google Scholar 

  40. Li X H, Duan X J, Sheng Y B, et al. Faithful quantum entanglement sharing based on linear optics with additional qubits. Chin Phys B, 2009, 18: 3710–3713

    Article  ADS  Google Scholar 

  41. Chen Q, Feng M. Quantum-information processing in decoherence-free subspace with low-Q cavities. Phys Rev A, 2010, 82: 052329

    Article  ADS  Google Scholar 

  42. Bennett C H, Brassard G, Popescu S, et al. Purification of noisy entanglement and faithful teleportation via noisy channels. Phys Rev Lett, 1996, 76: 722–725

    Article  ADS  Google Scholar 

  43. Pan J W, Simon C, Brukner C, et al. Entanglement purification for quantum communication. Nature, 2001, 410: 1067–1070

    Article  ADS  Google Scholar 

  44. Simo C, Pan J W. Polarization entanglement purification using spatial entanglement. Phys Rev Lett, 2002, 89: 257901

    Article  ADS  Google Scholar 

  45. Sheng Y B, Deng F G, Zhou H Y. Efficient polarization-entanglement purification based on parametric down-conversion sources with cross-Kerr nonlinearity. Phys Rev A, 2008, 77: 042308

    Article  ADS  Google Scholar 

  46. Sheng Y B, Deng F G, Zhou H Y. Nonlocal entanglement concentration scheme for partially entangled multipartite systems with nonlinear optics. Phys Rev A, 2008, 77: 062325

    Article  ADS  Google Scholar 

  47. Hughes R J, James D F V, Knill E H, et al. Decoherence bounds on quantum computation with trapped ions. Phys Rev Lett, 1996, 77: 3240–3243

    Article  ADS  Google Scholar 

  48. Cirac J I, Pellizzari T, Zoller P. Enforcing coherent evolution in dissipative quantum dynamics. Science, 1996, 273: 1207–1210

    Article  ADS  Google Scholar 

  49. van Enk S J, Cirac J I, Zoller P. Photonic channels for quantum communication. Science, 1998, 279: 205–208

    Article  ADS  Google Scholar 

  50. Qin S J, Wen Q Y, Meng L M, et al. Quantum secure direct communication over the collective amplitude damping channel. Sci China Ser G-Phys Mech Astron, 2009, 52: 1208–1212

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  52. Walgate J, Short A J, Hardy L, et al. Local distinguishability of multipartite orthogonal quantum states. Phys Rev Lett, 2000, 85: 4972–4975

    Article  ADS  Google Scholar 

  53. Li C Y, Li X H, Deng F G, et al. Efficient quantum cryptography network without entanglement and quantum memory. Chin Phys Lett, 2005, 22: 2896–2899

    Google Scholar 

  54. Li C Y, Zhou H Y, Wang Y, et al. Secure quantum key distribution network with Bell states and local unitary operations. Chin Phys Lett, 2006, 23: 1049–1052

    Google Scholar 

  55. Gisin N, Ribordy G, Tittel W, et al. Quantum cryptography. Rev Mod Phys, 2002, 74: 145–195

    Article  ADS  Google Scholar 

  56. Bennett C H, Brassad G. Quantum cryptography: Public key distribution and coin tossing. In: Proceedings of IEEE International Conference on Computers, Systems and Signal Processing, Bangalore, India. New York: IEEE, 1984. 175–179

    Google Scholar 

  57. Deng F G, Zhou P, Li X H. Robustness of two-way quantum communication protocols against Trojan horse attack. arXiv: quant-ph/0508168, 2005

  58. Cai Q Y. Eavesdropping on the two-way quantum communication protocols with invisible photons. Phys Lett A, 2006, 351: 23–25

    Article  ADS  MATH  Google Scholar 

  59. Li X H, Deng F G, Zhou H Y. Improving the security of secure direct communication based on the secret transmitting order of particles. Phys Rev A, 2006, 74: 054302

    Article  ADS  Google Scholar 

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Yang, Y., Chai, H., Wang, Y. et al. Fault tolerant quantum secret sharing against collective-amplitude-damping noise. Sci. China Phys. Mech. Astron. 54, 1619 (2011). https://doi.org/10.1007/s11433-011-4432-8

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  • DOI: https://doi.org/10.1007/s11433-011-4432-8

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