Skip to main content
Log in

Efficient entanglement concentration for arbitrary less-entangled NOON states

  • Published:
Quantum Information Processing Aims and scope Submit manuscript

Abstract

We put forward an efficient entanglement concentration protocol (ECP) for arbitrary less-entangled NOON state. In the protocol, we resort to the weak cross-Kerr nonlinearity to complete this task. Different from other ECPs, this protocol can be reused to get a high success probability. We do not need to know the exact coefficients of the initial state. Moreover, we even do not need to know the exact photon number of the initial NOON state. This protocol may be useful and convenient in the current quantum information processing.

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.

Institutional subscriptions

Similar content being viewed by others

References

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

    MATH  Google Scholar 

  2. Gisin N., Ribordy G., Tittel W., Zbinden H.: Quantum cryptography. Rev. Mod. Phys. 74, 145 (2002)

    Article  ADS  Google Scholar 

  3. Ekert A.K.: Quantum cryptography based on Bells theorem. Phys. Rev. Lett. 67, 661 (1991)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  4. Deng F.G., Long G.L.: Controlled order rearrangement encryption for quantum key distribution. Phys. Rev. A 68, 042315 (2003)

    Article  ADS  Google Scholar 

  5. Li X.H., Deng F.G., Zhou H.Y.: Efficient quantum key distribution over a collective noise channel. Phys. Rev. A 78, 022321 (2008)

    Article  ADS  Google Scholar 

  6. Bennett C.H., Brassard G., Mermin N.D.: Quantum cryptography without Bells theorem. Phys. Rev. Lett. 68, 557 (1992)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  7. Long G.L., Liu X.S.: Theoretically efficient high-capacity quantum-key-distribution scheme. Phys. Rev. A 65, 032302 (2002)

    Article  ADS  Google Scholar 

  8. Bennett C.H., Brassard G., Crepeau C., Jozsa R., Peres A., Wootters W.K.: Teleporting an unknown quantum state via dual classical and Einstein–Podolsky–Rosen channels. Phys. Rev. Lett. 70, 1895 (1993)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  9. Bouwmeester D., Pan J.W., Mattle K., Eibl M., Weinfurter H., Zeilinger A.: Experimental quantum teleportation. Nature 390, 575 (1997)

    Article  ADS  Google Scholar 

  10. 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 68, 042317 (2003)

    Article  ADS  Google Scholar 

  11. Wang C., Deng F.G., Li Y.S., Liu X.S., Long G. L.: Quantum secure direct communication with high-dimension quantum superdense coding. Phys. Rev. A 71, 044305 (2005)

    Article  ADS  Google Scholar 

  12. Divincenzo D.P.: Quantum computation. Science 270, 255 (1995)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  13. Bennett C.H., Divincenzo D.P.: Quantum information and computation. Nature (Lond.) 404, 247 (2000)

    Article  ADS  Google Scholar 

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

    Article  MathSciNet  ADS  MATH  Google Scholar 

  15. Hillery M., Bužek V., Berthiaume A.: Quantum secret sharing. Phys. Rev. A 59, 1829 (1999)

    Article  MathSciNet  ADS  Google Scholar 

  16. Karlsson A., Koashi M., Imoto N.: Quantum entanglement for secret sharing and secret splitting. Phys. Rev. A 59, 162 (1999)

    Article  ADS  Google Scholar 

  17. Xiao L., Long G.L., Deng F.G., Pan J.W.: Efficient multiparty quantum–secret–sharing schemes. Phys. Rev. A 69, 052307 (2004)

    Article  ADS  Google Scholar 

  18. Dowling J.P.: Quantum optical metrology-the lowdown on high-N00N states. Contemp. Phys. 49, 125 (2008)

    Article  ADS  Google Scholar 

  19. Huelga S.F., Macchiavello C., Pellizzari T., Ekert A.K.: Improvement of frequency standards with quantum entanglement. Phys. Rev. Lett. 79, 3865 (1997)

    Article  ADS  Google Scholar 

  20. Resch K.J., Pregnell K.L., Prevedel R., Gilchrist A., Pryde G.J., ÓBrien J.L., White A.G.: Time-reversal and super-resolving phase measurements. Phys. Rev. Lett. 98, 223601 (2007)

    Article  ADS  Google Scholar 

  21. Chen Y.A., Bao X.H., Yuan Z.S., Chen S., Zhao B., Pan J.W.: Heralded generation of an atomic NOON state. Phys. Rev. Lett. 104, 043601 (2010)

    Article  ADS  Google Scholar 

  22. Mitchell M.W., Lundeen J.S., Steinberg A.M.: Super-resolving phase measurements with a multiphoton entangled state. Nature 429, 161 (2004)

    Article  ADS  Google Scholar 

  23. Walther P., Pan J.W., Aspelmeyer M., Ursin R., Gasparoni S., Zeilinger A.: De Broglie wavelength of a non-local four-photon state. Nature 429, 158 (2004)

    Article  ADS  Google Scholar 

  24. Nagata T., Okamoto R., ÓBrien J.L., Sasaki K., Takeuchi S.: Beating the standard quantum limit with four-entangled photons. Science 316, 726 (2007)

    Article  ADS  Google Scholar 

  25. Israel Y., Afek I., Rosen S., Ambar O., Siberberg Y.: Experimental tomography of NOON states with large photon numbers. Phys. Rev. A 85, 022115 (2012)

    Article  ADS  Google Scholar 

  26. Greenberger D.M., Horne M.A., Shimony A., Zeilinger A.: Bells theorem without inequalities. Am. J. Phys. 58, 1131 (1990)

    Article  MathSciNet  ADS  Google Scholar 

  27. Mermin N.D.: Extreme quantum entanglement in a superposition of macroscopically distinct states. Phys. Rev. Lett. 65, 1838 (1990)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  28. Boto A.N., Kok P., Abrams D.S., Braunstein S.L., Williams C.P., Dowling J.P.: Quantum interferometric optical lithography: exploiting entanglement to beat the diffraction limit. Phys. Rev. Lett. 85, 2733 (2000)

    Article  ADS  Google Scholar 

  29. Bollinger J.J., Itano W.M., Wineland D.J., Heinzen D.J.: Optimal frequency measurements with maximally correlated states. Phys. Rev. A 54, R4649 (1996)

    Article  ADS  Google Scholar 

  30. Eckert K., Hyllus P., Bruss D. et al.: Differential atom interferometry beyond the standard quantum limit. Phys. Rev. A 73, 013814 (2006)

    Article  ADS  Google Scholar 

  31. D’Angelo M., Chekhova M.V., Shih Y.: Two-photon diffraction and quantum lithography. Phys. Rev. Lett. 87, 013602 (2001)

    Article  ADS  Google Scholar 

  32. Sun F.W., Ou Z.Y., Guo G.C.: Simple proof of fault tolerance in the graph-state model. Phys. Rev. A 73, 032308 (2006)

    Article  ADS  Google Scholar 

  33. Liu B., Ou Z.Y.: Feasibility of Bell tests with the W state. Phys. Rev. A 81, 033823 (2010)

    Article  ADS  Google Scholar 

  34. Bennett C.H., Bernstein H.J., Popescu S., Schumacher B.: Concentrating partial entanglement by local operations. Phys. Rev. A 53, 2046 (1996)

    Article  ADS  Google Scholar 

  35. Bose S., Vedral V., Knight P.L.: Purification via entanglement swapping and conserved entanglement. Phys. Rev. A 60, 194 (1999)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  40. Sheng Y.B., Deng F.G., Zhou H.Y.: Single-photon entanglement concentration for long distance quantum communication. Quant. Inf. Comput. 10, 272 (2010)

    MathSciNet  MATH  Google Scholar 

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

    Article  ADS  Google Scholar 

  42. Sheng Y.B., Zhou L., Zhao S.M.: Efficient two-step entanglement concentration for arbitrary W states. Phys. Rev. A 85, 044305 (2012)

    Google Scholar 

  43. Sheng Y.B., Deng F.G., Zhou H.Y.: Efficient polarization entanglement concentration for electrons with charge detection. Phys. Lett. A 373, 1823 (2009)

    Article  ADS  MATH  Google Scholar 

  44. Paunković N., Omar Y., Bose S., Vedral V.: Entanglement concentration using quantum statistics. Phys. Rev. Lett. 88, 187903 (2002)

    Article  ADS  Google Scholar 

  45. Wang X.B, Fan H.: Entanglement concentration by ordinary linear optical devices without postselection. Phys. Rev. A 68, 060302 (2003)

    Article  Google Scholar 

  46. Wang C., Zhang Y., Jin G.S.: Entanglement purification and concentration of electron-spin entangled states using quantum-dot spins in optical microcavities. Phys. Rev. A 84, 032307 (2011)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  48. Nemoto K., Munro W.J.: Nearly deterministic linear optical controlled-not gate. Phys. Rev. Lett. 93, 250502 (2004)

    Article  ADS  Google Scholar 

  49. Friedler I., Kurizki G., Petrosyan D.: Deterministic quantum logic with photons via optically induced photonic band gaps. Phys. Rev. A 71, 023803 (2005)

    Article  ADS  Google Scholar 

  50. Vitali D., Fortunato M., Tombesi P.: Complete quantum teleportation with a kerr nonlinearity. Phys. Rev. Lett. 85, 445 (2000)

    Article  ADS  Google Scholar 

  51. 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 77, 042308 (2008)

    Article  ADS  Google Scholar 

  52. Sheng Y.B., Deng F.G.: Deterministic entanglement purification and complete nonlocal Bell-state analysis with hyperentanglement. Phys. Rev. A 81, 032307 (2010)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  56. He B., Ren Y.H., Bergou J.A.: Universal entangler with photon pairs in arbitrary states. J. Phys. B 43, 025502 (2010)

    Article  ADS  Google Scholar 

  57. He B., Lin Q., Simon C.: Cross-Kerr nonlinearity between continuous-mode coherent states and single photons. Phys. Rev. A 83, 053826 (2011)

    Article  ADS  Google Scholar 

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

    Article  MathSciNet  ADS  Google Scholar 

  59. Lin Q., He B.: Single-photon logic gates using minimal resources. Phys. Rev. A 80, 042310 (2009)

    Article  ADS  Google Scholar 

  60. Lin Q., He B., Bergou J.A., Ren Y.H.: Processing multiphoton states through operation on a single photon: Methods and applications. Phys. Rev. A 80, 042311 (2009)

    Article  ADS  Google Scholar 

  61. Lin Q., He B.: Bi-directional mapping between polarization and spatially encoded photonic qutrits. Phys. Rev. A 80, 062312 (2009)

    Article  ADS  Google Scholar 

  62. Lin Q., He B.: Efficient generation of universal two-dimensional cluster states with hybrid systems. Phys. Rev. A 82, 022331 (2010)

    Article  ADS  Google Scholar 

  63. Lin Q., He B.: Addendum to “single-photon logic gates using minimum resources”. Phys. Rev. A 82, 064303 (2010)

    Article  ADS  Google Scholar 

  64. Li Y.M., Zhang K.S., Peng K.C.: Generation of qudits and entangled qudits. Phys. Rev. A 77, 015802 (2008)

    Article  ADS  Google Scholar 

  65. Jeong H., An N.B.: Greenberger–Horne–Zeilinger-type and W-type entangled coherent states: Generation and Bell-type inequality tests without photon counting. Phys. Rev. A 74, 022104 (2006)

    Article  MathSciNet  ADS  Google Scholar 

  66. Guo Q., Bai J., Cheng L.Y., Shao X.Q., Wang H.F., Zhang S.: Simplified optical quantum-information processing via weak cross-Kerr nonlinearities. Phys. Rev. A 83, 054303 (2011)

    Article  ADS  Google Scholar 

  67. Sheng Y.B., Deng F.G., Long G.L.: Complete hyperentangled-Bell-state analysis for quantum communication. Phys. Rev. A 82, 032318 (2010)

    Article  ADS  Google Scholar 

  68. Jin G.S., Lin Y., Wu B.: Generating multiphoton Greenberger–Horne–Zeilinger states with weak cross-Kerr nonlinearity. Phys. Rev. A 75, 054302 (2007)

    Article  ADS  Google Scholar 

  69. Wang W.W., Zhang D.Y., Tang S.Q., Xie L.J., Wang Z.Y., Kuang L.M.: Photonic two-qubit parity gate with tiny cross-Kerr nonlinearity. Phys. Rev. A 85, 052326 (2012)

    Article  ADS  Google Scholar 

  70. Barrett S.D., Kok P., Nemoto K., Beausoleil R.G., Munro W.J., Spiller T.P.: Symmetry analyzer for nondestructive Bell-state detection using weak nonlinearities. Phys. Rev. A 71, 060302 (2005)

    Article  ADS  Google Scholar 

  71. Nielsen A.E.B., Giedke G.M.A., Vollbrecht K.G.H.: Quantum state engineering, purification, and number-resolved photon detection with high-finesse optical cavities. Phys. Rev. A 81, 043823 (2010)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  74. Kok P., Munro W.J., Nemoto K., Ralph T.C., Dowing J.P., Milburn G.J.: Linear optical quantum computing with photonic qubits. Rev. Mod. Phys. 79, 135 (2007)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  76. Hofmann H.F., Kojima K., Takeuchi S., Sasaki K.: Optimized phase switching using a single-atom nonlinearity. J. Opt. B 5, 218 (2003)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Yu-Bo Sheng.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Zhou, L., Sheng, YB., Cheng, WW. et al. Efficient entanglement concentration for arbitrary less-entangled NOON states. Quantum Inf Process 12, 1307–1320 (2013). https://doi.org/10.1007/s11128-012-0472-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11128-012-0472-x

Keywords

Navigation