Skip to main content
Log in

Efficient N-particle W state concentration with different parity check gates

  • Article
  • Quantum Physics
  • Published:
Science China Physics, Mechanics & Astronomy Aims and scope Submit manuscript

Abstract

We present a universal way to concentrate an arbitrary N-particle less-entangled W state into a maximally entangled W state with different parity check gates. It comprises two protocols. The first protocol is based on the linear optical elements, say the partial parity check gate and the second protocol uses the quantum nondemolition measurement to construct the complete parity check gate. Both protocols can achieve the concentration task. These protocols have several advantages. First, they can obtain a maximally entangled W state only with the help of some single photons, which greatly reduces the number of entanglement resources. Second, in the first protocol, only linear optical elements are required, which is feasible with current techniques. Third, the second protocol can be repeated to perform the concentration step and obtain a higher success probability. All these advantages make it quite useful in current quantum communication and computation applications.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

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

    MATH  Google Scholar 

  2. Lin Q. Optical parity gate and a wide range of entangled states generation. Sci China-Phys Mech Astron, 2015, 58: 044201

    Article  Google Scholar 

  3. Heilmann R, Gräfe M, Nolte S, et al. A novel integrated quantum circuit for high-order W-state generation and its highly precise characterization. Sci Bull, 2015, 60: 96–100

    Article  Google Scholar 

  4. Xu J S, Li C F. Quantum integrated circuit: Classical characterization. Sci Bull, 2015, 60: 141–141

    Article  Google Scholar 

  5. Bennett C H, Brassard G, Crepeau C, et al. Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels. Phys Rev Lett, 1993, 70: 1895–1899

    Article  ADS  MATH  MathSciNet  Google Scholar 

  6. Ekert A K. Quantum cryptography based on Bell’s theorem. Phys Rev Lett, 1991, 67: 661–663

    Article  ADS  MATH  MathSciNet  Google Scholar 

  7. Bennett C H, Wiesner S J. Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states. Phys Rev Lett, 1992, 69: 2881–2884

    Article  ADS  MATH  MathSciNet  Google Scholar 

  8. Liu X S, Long G L, Tong D M, et al. General scheme for superdense coding between multiparties. Phys Rev A, 2002, 65: 022304

    Article  ADS  Google Scholar 

  9. 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 

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

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  Google Scholar 

  12. Long G L, Liu X S. Theoretically efficient high-capacity quantumkeydistribution scheme. Phys Rev A, 2002, 65: 032302

    Article  ADS  Google Scholar 

  13. Deng F G, Long G L, Liu X S. Two-step quantum direct communication protocol using the Einstein-Podolsky-Rosen pair block. Phys Rev A, 2003, 68: 042317

    Article  ADS  Google Scholar 

  14. Wang C, Deng F G, Li Y S, et al. Quantum secure direct communication with high-dimension quantum superdense coding. Phys Rev A, 2005, 71: 044305

    Article  ADS  Google Scholar 

  15. Zou X F, Qiu D W. Three-step semiquantum secure direct communication protocol. Sci China-Phys Mech Astron, 2014, 57: 1696–1702

    Article  ADS  Google Scholar 

  16. Chang Y, Xu C, Zhang S, et al. Controlled quantum secure direct communication and authentication protocol based on five-particle cluster state and quantum one-time pad. Chin Sci Bull, 2014, 59: 2541–2546

    Article  Google Scholar 

  17. Chang Y, Xu C X, Zhang S B, et al. Quantum secure direct communication and authentication protocol with single photons. Chin Sci Bull, 2013, 58: 4571–4576

    Article  Google Scholar 

  18. Zheng C, Long G F. Quantum secure direct dialogue using Einstein-Podolsky-Rosen pairs. Sci China-Phys Mech Astron, 2014, 57: 1238–1243

    Article  ADS  Google Scholar 

  19. 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 

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

    Article  ADS  Google Scholar 

  21. Simon C, Pan JW. Polarization entanglement purification using spatial entanglement. Phys Rev Lett, 2002, 89: 257901

    Article  ADS  Google Scholar 

  22. Sheng Y B, Zhou L, Long G L. Hybrid entanglement purification for quantum repeaters. Phys Rev A, 2013, 88: 022302

    Article  ADS  Google Scholar 

  23. Sheng Y B, Zhou L. Deterministic polarization entanglement purification using time-bin entanglement. Laser Phys Lett, 2014, 11: 085203

    Article  ADS  Google Scholar 

  24. Wang C, Zhang Y, Jin G S. Polarization-entanglement purification and concentration using cross-Kerr nonlinearity. Quantum Inform Comput, 2011, 11: 988–1002

    MATH  MathSciNet  Google Scholar 

  25. Wang C, Zhang Y, Zhang R. Entanglement purification based on hybrid entangled state using quantum-dot and microcavity coupled system. Opt Exp, 2011, 19: 25685–25695

    Article  ADS  Google Scholar 

  26. Li X H. Deterministic polarization-entanglement purification using spatial entanglement. Phys Rev A, 2010, 82: 044304

    Article  ADS  Google Scholar 

  27. Ren B C, Du F F, Deng F G. Two-step hperentanglement purification with the quantum-state-joining method. Phys Rev A, 2014, 90: 052309

    Article  ADS  Google Scholar 

  28. Hou S Y, Sheng Y B, Feng G R, et al. Experimental optimal single qubit purification in an NMR quantum information processor. Sci Rep, 2014, 4: 6857

    Article  ADS  Google Scholar 

  29. Sheng Y B, Zhou L. Deterministic entanglement distillation for secure double-server blind quantum computation. Sci Rep, 2014, 5: 7815

    Article  Google Scholar 

  30. Bennett C H, Bernstein H J, Popescu S, et al. Concentrating partial entanglement by local operations. Phys Rev A, 1996, 53: 2046–2052

    Article  ADS  Google Scholar 

  31. Bose S, Vedral V, Knight P L. Purification via entanglement swapping and conserved entanglement. Phys Rev A, 1999, 60: 194–197

    Article  ADS  Google Scholar 

  32. Shi B S, Jiang Y K, Guo G C. Optimal entanglement purification via entanglement swapping. Phys Rev A, 2000, 62: 054301

    Article  ADS  Google Scholar 

  33. Yamamoto T, Koashi M, Imoto N. Concentration and purification scheme for two partially entangled photon pairs. Phys Rev A, 2001, 64: 012304

    Article  ADS  Google Scholar 

  34. Zhao Z, Pan J W, Zhan M S. Practical scheme for entanglement concentration. Phys Rev A, 2001, 64: 014301

    Article  ADS  Google Scholar 

  35. 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 

  36. Sheng Y B, Zhou L, Zhao S M, et al. Efficient single-photon-assisted entanglement concentration for partially entangled photon pairs. Phys Rev A, 2012, 85: 012307

    Article  ADS  Google Scholar 

  37. Deng F G. Optimal nonlocal multipartite entanglement concentration based on projection measurements. Phys Rev A, 2012, 85: 022311

    Article  ADS  Google Scholar 

  38. Wang C. Efficient entanglement concentration for partially entangled electrons using a quantum-dot and microcavity coupled system. Phys Rev A, 2012, 86: 012323

    Article  ADS  Google Scholar 

  39. Cao C, Wang C, He L Y, et al. Atomic entanglement purification and concentration using coherent state input-output process in low-Q cavity QED regime. Opt Exp, 2013, 21: 4093–4105

    Article  ADS  Google Scholar 

  40. Xiong W, Ye L. Schemes for entanglement concentration of two unknown partially entangled states with cross-Kerr nonlinearity. J Opt Soc Am B, 2011, 28: 2030–2037

    Article  ADS  Google Scholar 

  41. Wang C, Cao C, He L Y, et al. Hybrid entanglement concnetration using quantum dot and microcavity coupled system. Quantum Inf Process, 2014, 13: 1025–1034

    Article  ADS  MATH  MathSciNet  Google Scholar 

  42. Sheng Y B, Zhou L. Quantum entanglement concentration based on linear optics for quantum communications. Entropy, 2013, 15: 1776–1820

    Article  ADS  MATH  MathSciNet  Google Scholar 

  43. Ren B C, Du F F, Deng F G. Hyperentanglement concentration for two-photon four-qubit systems with linear optics. Phys Rev A, 2013, 88: 012302

    Article  ADS  Google Scholar 

  44. Ren B C, Deng F G. Hyperentanglement purification and concentration assisted by diamond NV centers inside photonic crystal cavities. Laser Phys Lett, 2013, 10: 115201

    Article  ADS  Google Scholar 

  45. Ren B C, Long G L. General hyperentanglement concentration for photon systems assisted by quantum-dot spins inside optical microcavities. Opt Exp, 2014, 22: 6547–6561

    Article  ADS  Google Scholar 

  46. Li X H, Ghose S. Hyperconcentration for multipartite entanglement via linear optics. Laser Phys Lett, 2014, 11: 125201

    Article  ADS  Google Scholar 

  47. Du F F, Deng F G. Heralded entanglement concentration for photon systems with linear-optical elements. Sci China-Phys Mech Astron, 2015, 58: 040303

    Google Scholar 

  48. Zhao J, Zheng C H, Shi P, et al. Generation and entanglement concentration for electron-spin entangled cluster states using charged quantum dots in optical microcavities. Opt Commun, 2014, 322: 32–39

    Article  ADS  Google Scholar 

  49. Zhou L. Consequent entanglement concentration of a less-entangled electronic cluster state with controlled-not gates. Chin Phys B, 2014, 23: 050308

    Article  Google Scholar 

  50. Si B, Wen J J, Cheng L Y, et al. Efficient entanglement concentration schemes for separated nitrogen-vacancy centers coupled to low-Q microresonators. Int J Theor Phys, 2014, 53: 80–90

    Article  MATH  Google Scholar 

  51. Choudhury B S, Dhara A. A three-qubit state entanglement concentration protocol assisted by two-qubit systems. Int J Theor Phys, 2013, 52: 3965–3969

    Article  MATH  MathSciNet  Google Scholar 

  52. Si B, Su S L, Sun L L, et al. Efficient three-step entanglement concentration for an arbitrary four-photon cluster state. Chin Phys B, 2013, 22: 030305

    Article  ADS  Google Scholar 

  53. Zheng S B. Splitting quantum information via W states. Phys Rev A, 2006, 74: 054303

    Article  ADS  Google Scholar 

  54. Agrawal P, Pati A. Perfect teleportation and superdense coding with W states. Phys Rev A, 2006, 74: 062320

    Article  ADS  Google Scholar 

  55. Song J, Xia Y, Song H S. Quantum nodes for W-state generation in noisy channels. Phys Rev A, 2008, 78: 024302

    Article  ADS  Google Scholar 

  56. Tamaryan L, Ohanyan Z, Tamaryan S. Universal behavior of the geometric entanglement measure of many-qubit W states. Phys Rev A, 2010, 82: 022309

    Article  ADS  Google Scholar 

  57. Eibl M, Kiesel N, Bourennane M, et al. Experimental realization of a three-qubit entangled W state. Phys Rev Lett, 2004, 92: 077901

    Article  ADS  Google Scholar 

  58. Tashima T, Wahatsuki T, Özdemir S K, et al. Local transformation of two Einstein-Podolsky-Rosen photon pairs into a three-photon W state. Phys Rev Lett, 2009, 102: 130502

    Article  ADS  MathSciNet  Google Scholar 

  59. Cao Z L, Yang M. Entanglement distillation for three-particle W class states. J Phys B, 2003, 36: 4245

    Article  ADS  Google Scholar 

  60. Zhang L H, Yang M, Cao Z L. Entanglement concentration for unknown W class states. Phys A, 2007, 374: 611–616

    Article  Google Scholar 

  61. Wang H F, Zhang S, Yeon K H. Linear optical scheme for entanglement concentration of two partially entangled three-photon W states. Eur Phys J D, 2010, 56: 271–275

    Article  ADS  Google Scholar 

  62. Yildiz A. Optimal distillation of three-qubit W states. Phys Rev A, 2010, 82: 012317

    Article  ADS  Google Scholar 

  63. Sheng Y B, Zhou L, Zhao S M. Efficient two-step entanglement concentration for arbitrary W states. Phys Rev A, 2012, 85: 042302

    Article  ADS  Google Scholar 

  64. Du F F, Li T, Ren B C, et al. Single-photon-assisted entanglement concentration of a multiphoton system in a partially entangled W state with weak cross-Kerr nonlinearity. J Opt Soc Am B, 2012, 29: 1399–1405

    Article  ADS  Google Scholar 

  65. Zhou L. Efficient entanglement concnetration for electron-spin W state with the charge detection. Quantum Inf Process, 2013, 12: 2087–2101

    Article  ADS  MATH  MathSciNet  Google Scholar 

  66. Gu B, Duan D H, Xiao S R. Multi-photon entanglement concentration protocol for partially entangled W states with projection measurement. Int J Theor Phys, 2012, 51: 2966–2973

    Article  MATH  Google Scholar 

  67. Gu B. Single-photon-assisted entanglement concentration of partially entangled multiphoton W states with linear optics. J Opt Soc Am B, 2012, 29: 1685–1689

    Article  ADS  Google Scholar 

  68. Zhou L, Sheng Y B, Cheng WW, et al. Efficient entanglement concentration for arbitrary less-entangled NOON states. Quantum Inf Process, 2013, 12: 1307–1320

    Article  ADS  MATH  MathSciNet  Google Scholar 

  69. Fan L L, Xia Y, Song J. Efficient entanglement concentration for arbitrary less-hyperentanglement multi-photon W states with linear optics. Quantum Inf Process, 2014, 13: 1967–1978

    Article  ADS  MATH  MathSciNet  Google Scholar 

  70. Want T J, Long G L. Entanglement concentration for arbitrary unknown less-entangled three-photon W states with linear optics. J Opt Soc Am B, 30: 1069–1076

  71. Ji Y Q, Jin Z, Zhu A D, et al. Concentration of multi-photon entanglement with linear optics assisted by quantum nondemolition detection. J Opt Soc Am B, 2014, 31: 994–999

    Article  ADS  Google Scholar 

  72. Zhang R, Zhou S H, Cao C. Efficient nonlocal two-step entanglement concentration protocol for three-level atoms in an arbitrary lessentangled W state using cavity input-output process. Sci China-Phys Mech Astron, 2014, 57: 1511–1518

    Article  ADS  Google Scholar 

  73. Sheng Y B, Liu J, Zhao S Y, et al. Multipartite entanglement concentration for nitrogen-vacancy center and microtoroidal resonator system. Chin Sci Bull, 2013, 59: 3507–3513

    Article  Google Scholar 

  74. Sheng Y B, Liu J, Zhao S Y, et al. Entanglement concentration for W-type entangled coherent states. Chin Phys B, 2014, 23: 080305

    Article  ADS  Google Scholar 

  75. Zhou L, Sheng Y B, Zhao S M. Optimal entanglement concentration for three-photon W states with parity check measurement. Chin Phys B, 2013, 22: 020307

    Article  ADS  Google Scholar 

  76. Zhou L, Sheng Y B, Cheng WW, et al. Efficient entanglement concentration for arbitrary single-photon multimode W state. J Opt Soc Am B, 2013, 30: 71–78

    Article  ADS  Google Scholar 

  77. Pittman T B, Jacobs B C, Franson J D. Probabilistic quantum logic operations using polarizing beam splitters. Phys Rev A, 2001, 64: 062311

    Article  ADS  Google Scholar 

  78. Nemoto K, Munro W J. Nearly deterministic linear optical controllednot gate. Phys Rev Lett, 2004, 93: 250502

    Article  ADS  Google Scholar 

  79. Barrett S D, Kok P, Nemoto K, et al. Symmetry analyzer for nondestructive Bell-state detection using weak nonlinearities. Phys Rev A, 2005, 71: 060302

    Article  ADS  Google Scholar 

  80. Lin Q, Li J. Quantum control gates with weak cross-Kerr nonlinearity. Phys Rev A, 2009, 79: 022301

    Article  ADS  Google Scholar 

  81. He B, Bergou J A, Ren Y H. Universal discriminator for completely unknown optical qubits. Phys Rev A, 2007, 76: 032301

    Article  ADS  Google Scholar 

  82. He B, Nadeem M, Bergou J A. Scheme for generating coherent-state superpositions with realistic cross-Kerr nonlinearity. Phys Rev A, 2009, 79: 035802

    Article  ADS  Google Scholar 

  83. He B, Ren Y H, Bergou J A. Creation of high-quality long-distance entanglement with flexible resources. Phys Rev A, 2009, 79: 052323

    Article  ADS  Google Scholar 

  84. He B, Lin Q, Simon C. Cross-Kerr nonlinearity between continuousmode coherent states and single photons. Phys Rev A, 2011, 83: 053826

    Article  ADS  Google Scholar 

  85. Dong L, Xiu X M, Gao Y J, et al. A nearly deterministic scheme for generating chi-type entangled states with weak cross-Kerr nonlinearities. Quantum Inf Process, 2013, 12: 1787–1795

    Article  ADS  MATH  MathSciNet  Google Scholar 

  86. Xiu X M, Dong L, Shen H Z, et al. Construction scheme of a twophoton polarization controlled arbitrary phase gate mediated by weak cross-phase modulation. J Opt Soc Am B, 2013, 30: 589–597

    Article  ADS  Google Scholar 

  87. Dong L, Wang J X, Shen H Z, et al. Deterministic transmission of an arbitrary single-photon polarization state through bit-flip error channel. Quantum Inf Process, 2014, 13: 1413–1424

    Article  ADS  MATH  MathSciNet  Google Scholar 

  88. Xiu X M, Dong L, Shen H Z, et al. Two-party quantum privacy comparison with polarization-entangled Bell state and the coherent states. Quantum Inf Comput, 2014, 14: 236–254

    MathSciNet  Google Scholar 

  89. Kok P, Munro WJ, Nemoto K, et al. Linear optical quantum computing with photonic qubits. Rev Mod Phys, 2007, 79: 135–174

    Article  ADS  Google Scholar 

  90. Kok P, Lee H, Dowling J P. Single-photon quantum-nondemolition detectors constructed with linear optics and projective measurements. Phys Rev A, 2002, 66: 063814

    Article  ADS  Google Scholar 

  91. Gea-Banacloche J. Impossibility of large phase shifts via the giant Kerr effect with single-photon wave packets. Phys Rev A, 2010, 81: 043823

    Article  ADS  Google Scholar 

  92. Shapiro J H. Single-photon Kerr nonlinearities do not help quantum computation. Phys Rev A, 2006, 73: 062305

    Article  ADS  Google Scholar 

  93. Shapiro J H, Razavi M. Continuous-time cross-phase modulation and quantum computation. New J Phys, 2007, 9: 16

    Article  Google Scholar 

  94. Hofmann H F, Kojima K, Takeuchi S, et al. Optimized phase switching using a single-atom nonlinearity. J Opt B, 2003, 5: 218

    Article  ADS  Google Scholar 

  95. Feizpour A, Xing X, Steinberg A M. Amplifying single-photon nonlinearity using weak measurements. Phys Rev Lett, 2011, 107: 133603

    Article  ADS  Google Scholar 

  96. Zhu C J, Huang G X. Giant Kerr nonlinearity, controlled entangled photons and polarization phase gates in coupled quantum-well structures. Opt Exp, 2011, 19: 23364

    Article  ADS  Google Scholar 

  97. Venkataraman V, Saha K, Gaeta A L. Phase modulation at the fewphoton level for weak-nonlinearity-based quantum computing. Nat Photon, 2013, 7: 138–141

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to YuBo Sheng.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Sheng, Y., Pan, J., Guo, R. et al. Efficient N-particle W state concentration with different parity check gates. Sci. China Phys. Mech. Astron. 58, 1–11 (2015). https://doi.org/10.1007/s11433-015-5672-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11433-015-5672-9

Keywords

Navigation