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Classical communication cost and probabilistic remote two-qubit state preparation via POVM and W-type states

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Abstract

I present a new scheme for probabilistic remote preparation of a general two-qubit state by using two W-type states as the shared quantum channel and a proper POVM instead of the usual positive measurement. Also I explore the scheme’s applications to five special ensembles of two-qubit states. The success probability and the classical communication cost in different cases are calculated minutely, respectively, which show that the remote two-qubit preparation can be realized with higher probability after consuming some more classical bits provided that the two-qubit state to be prepared is chosen from the special ensembles.

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References

  1. 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  ADS  MathSciNet  MATH  Google Scholar 

  2. Lo H.K.: Classical-communication cost in distributed quantum-information processing: a generalization of quantum-communication complexity. Phys. Rev. A 62, 012313 (2000)

    Article  ADS  Google Scholar 

  3. Pati A.K.: Minimum classical bit for remote preparation and measurement of a qubit. Phys. Rev. A 63, 014302 (2001)

    Article  ADS  Google Scholar 

  4. Bennett C.H. et al.: Remote state preparation. Phys. Rev. Lett. 87, 077902 (2001)

    Article  ADS  Google Scholar 

  5. Devetak I., Berger T.: Low-entanglement remote state preparation. Phys. Rev. Lett. 87, 177901 (2001)

    Article  ADS  Google Scholar 

  6. Zeng B., Zhang P.: Remote-state preparation in higher dimension and the parallelizable manifold Sn−1. Phys. Rev. A 65, 022316 (2002)

    Article  ADS  Google Scholar 

  7. Berry D.W., Sanders B.C.: Optimal remote state preparation. Phys. Rev. Lett. 90, 027901 (2003)

    Article  Google Scholar 

  8. Kurucz Z., Adam P., Janszky J.: General criterion for oblivious remote state preparation. Phys. Rev. A 73, 062301 (2006)

    Article  ADS  Google Scholar 

  9. Hayashi A., Hashimoto T., Horibe M.: Remote state preparation without oblivious conditions. Phys. Rev. A 67, 052302 (2003)

    Article  ADS  Google Scholar 

  10. Abeyesinghe A., Hayden P.: Generalized remote state preparation: trading cbits, qubits, and ebits in quantum communication. Phys. Rev. A 68, 062319 (2003)

    Article  ADS  Google Scholar 

  11. Ye M.Y., Zhang Y.S., Guo G.C.: Faithful remote state preparation using finite classical bits and a nonmaximally entangled state. Phys. Rev. A 69, 022310 (2004)

    Article  ADS  Google Scholar 

  12. Yu Y.F., Feng J., Zhan M.S.: Preparing remotely two instances of quantum state. Phys. Lett. A 310, 329 (2003)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  13. Huang Y.X., Zhan M.S.: Remote preparation of multipartite pure state. Phys. Lett. A 327, 404 (2004)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  14. Paris M.G.A., Cola M., Bonifacio R.: Remote state preparation and teleportation in phase space. J. Opt. B 5, S360 (2003)

    Article  ADS  Google Scholar 

  15. Kurucz Z., Adam P., Kis Z., Janszky J.: Continuous variable remote state preparation. Phys. Rev. A 72, 052315 (2005)

    Article  ADS  Google Scholar 

  16. Babichev S.A., Brezger B., Lvovsky A.I.: Remote preparation of a single-mode photonic qubit by measuring field quadrature noise. Phys. Rev. Lett. 92, 047903 (2004)

    Article  ADS  Google Scholar 

  17. Gour G., Sanders B.C.: Remote preparation and distribution of bipartite entangled states. Phys. Rev. Lett. 93, 260501 (2004)

    Article  ADS  Google Scholar 

  18. Berry D.W.: Resources required for exact remote state preparation. Phys. Rev. A 70, 062306 (2004)

    Article  ADS  Google Scholar 

  19. Bennett C.H., Hayden P., Leung D.W., Shor P.W., Winter A.: Remote preparation of quantum states. IEEE Trans. Inform. Theory 51, 56 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  20. Xu L.L., Yu Y.F., Zhang Z.M.: Scheme for the preparation of entanglement for atomic ensembles. Int. J. Quantum Inf. 7, 1459 (2009)

    Article  MATH  Google Scholar 

  21. Peng X.H., Zhu X., Fang X., Feng M., Liu M., Gao K.: Experimental implementation of remote state preparation by nuclear magnetic resonance . Phys. Lett. A 306, 271 (2003)

    Article  ADS  Google Scholar 

  22. Xiang G.Y., Li J., Bo Y., Guo G.C.: Remote preparation ofmixed states via noisy entanglement. Phys. Rev. A 72, 012315 (2005)

    Article  ADS  Google Scholar 

  23. Peters N.A., Barreiro J.T., Goggin M.E., Wei T.C., Kwiat P.G.: Remote state preparation: arbitrary remote control of photon polarization. Phys. Rev. Lett. 94, 150502 (2005)

    Article  ADS  Google Scholar 

  24. Shi B.S., Tomita A.: Remote state preparation of an entangled state. J. Opt. B 4, 380 (2002)

    Article  ADS  MathSciNet  Google Scholar 

  25. Liu J.M., Wang Y.Z.: Remote preparation of a two-particle entangled state. Phys. Lett. A 316, 159 (2003)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  26. Liu J.M., Feng X.L., Oh C.H.: Remote preparation of a three-particle state via positive operator- valued measurement. J. Phys. B 42, 055508 (2009)

    Article  ADS  Google Scholar 

  27. Liu J.M., Feng X.L., Oh C.H.: Remote preparation of arbitrary two- and three-qubit states. Eur. Phys. Lett. 87, 30006 (2009)

    Article  ADS  Google Scholar 

  28. Xiao X.Q., Liu J.M.: Remote preparation of a two-particle entangled state by a bipartite entangled state and a tripartite entangled W state. Commun. Theor. Phys. 47, 247 (2007)

    Article  ADS  MATH  Google Scholar 

  29. Xiao X.Q., Liu J.M.: Remote preparation of a two-particle entangled state via two tripartite W entangled states. Int. J. Theor. Phys. 46, 2378 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  30. Yu C.S., Song H.S., Wang Y.H.: Remote preparation of a qudit using maximally entangled states of qubits. Phys. Rev. A 73, 022340 (2006)

    Article  ADS  Google Scholar 

  31. Xia Y, Song J., Song H.S.: Multiparty remote state preparation. J. Phys. B At. Mol. Opt. Phys. 40, 3719 (2007)

    Article  ADS  Google Scholar 

  32. Xia Y, Song J., Song H.S.: Remote preparation of the N-particle GHZ state using quantum statistics. Opt. Commun. 277, 219 (2007)

    Article  ADS  Google Scholar 

  33. Wang Y.H., Song H.S.: Preparation of partially entangled W state and deterministic multi-controlled teleportation. Opt. Commun. 281, 489 (2008)

    Article  ADS  Google Scholar 

  34. Zhang Y.Q., Jin X.R., Zhang S.: Probabilistic remote preparation of a two-atom entangled state. Chin. Phys. B 14, 1732 (2005)

    Article  ADS  Google Scholar 

  35. Yan F.L., Zhang G.H.: Remote preparation of the two-particle state. Int. J. Quantum Inf. 6, 485 (2008)

    Article  MATH  Google Scholar 

  36. Dai H.Y., Chen P.X., Liang L.M., Li C.Z.: Classical communication cost and remote preparation of the four-particle GHZ class state. Phys. Lett. A 355, 285 (2006)

    Article  ADS  Google Scholar 

  37. Dai H.Y., Chen P.X., Zhang M., Li C.Z.: Remote preparation of an entangled two-qubit state with three parties. Chin. Phys. B 17, 28 (2008)

    ADS  Google Scholar 

  38. Zhan Y.B.: Remote state preparation of a Greenberger-Horne-Zeilinger class state. Commun. Theor. Phys. 43, 637 (2005)

    Article  ADS  MathSciNet  Google Scholar 

  39. Ma P.C., Zhan Y.B.: Scheme for probabilistic remotely preparing a multi-particle entangled GHZ state. Chin. Phys. B 17, 445 (2008)

    Article  ADS  Google Scholar 

  40. Ma P.C., Zhan Y.B.: Scheme for remotely preparing a four-particle entangled cluster-type state. Opt. Commun. 283, 2640 (2010)

    Article  ADS  Google Scholar 

  41. Hou K., Wang J., Shi S.H.: Probabilistic remote preparation an arbitrary two-particle entangled state via positive operator-valued measure. Int. J. Quantum Inf. 6, 1183 (2008)

    Article  MATH  Google Scholar 

  42. Wang D., Liu Y.M., Zhang Z.J.: Remote preparation of a class of three-qubit states. Opt. Commun. 281, 871 (2008)

    Article  ADS  Google Scholar 

  43. Zhang W, Liu Y.M., Yin X.F., Zhang Z.J.: Splitting four ensembles of two-qubit quantum information via three Einstein-Podolsky-Rosen pairs. Eur. Phys. J. D 55, 189 (2009)

    Article  ADS  Google Scholar 

  44. Wang Z.Y., Liu Y.M., Zuo X.Q., Zhang Z.J.: Controlled remote state preparation. Commun. Theor. Phys. 52, 235 (2009)

    Article  ADS  MATH  Google Scholar 

  45. Wang Z.Y.: Controlled remote preparation of a two-qubit state via an asymmetric quantum channel. Commun. Theor. Phys. 55, 244 (2011)

    Article  ADS  MATH  Google Scholar 

  46. Wang Z.Y.: Symmetric remote single-qubit state preparation via positive operator-valued measurement. Int. J. Theor. Phys. 49, 1357 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  47. Wang Z.Y.: Joint remote preparation of a multi-qubit GHZ-class state via bipartite entanglements. Int. J. Quant. Inform. 9, 809 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  48. An N.B., Kim J.: Joint remote state preparation. J. Phys. B 41, 095501 (2008)

    Article  ADS  Google Scholar 

  49. An N.B.: Joint remote preparation of a general two-qubit state. J. Phys. B 42, 125501 (2009)

    Article  ADS  Google Scholar 

  50. An N.B.: Joint remote state preparation via W and W-type states. Opt. Commun. 283, 4113 (2010)

    Article  ADS  Google Scholar 

  51. Chen Q.Q., Xia Y., An N.B.: Joint remote preparation of an arbitrary three-qubit state via EPR-type pairs. Opt. Commun. 284, 2617 (2011)

    Article  ADS  Google Scholar 

  52. Luo M.X., Chen X.B., Ma S.Y., Yang Y.X., Hu Z.M.: Deterministic remote preparation of an arbitrary W-class state with multiparty. J. Phys. B 43, 065501 (2010)

    Article  ADS  Google Scholar 

  53. Luo M.X., Chen X.B., Ma S.Y., Yang Y.X., Niu X.X.: Joint remote preparation of an arbitrary three-qubit state. Opt. Commun. 283, 497–501 (2010)

    Article  ADS  Google Scholar 

  54. Luo M.X., Chen X.B., Ma S.Y., Yang Y.X., Hu Z.M.: Remote preparation of an arbitrary two-qubit state with three-party. Int. J. Theor. Phys. 49, 1262 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  55. Li W.L., Li C.F., Guo G.C.: Probabilistic teleportation and entanglement matching. Phys. Rev. A 61, 034301 (2000)

    Article  ADS  Google Scholar 

  56. Helstrom C.W.: Quantum Dectection and Estimation Theory. Academic Press, New York (1976)

    MATH  Google Scholar 

  57. Mar, T., Horodecki, P.: Teleportation via generalized measurements, and conclusive teleportation. quant-ph/9906039

  58. Yan F.L., Ding H.W.: Probabilistic teleportation of an unknown two-particle state with a four-particle pure entangled state and positive operator valued measure. Chin. Phys. Lett. 23, 17 (2006)

    Article  ADS  Google Scholar 

  59. Gu Y.J.: Deterministic exact teleportation via two partially entangled pairs of particles. Opt. Commun. 259, 385 (2006)

    Article  ADS  Google Scholar 

  60. Greenberger M., Horne M.A., Zeilinger A.A.: Bell’s theorem without inequalities. J. Phys. 58, 1131 (1990)

    ADS  MathSciNet  MATH  Google Scholar 

  61. Dur W., Vidal G., Cirac J.I.: Three qubits can be entangled in two inequivalent ways. Phys. Rev. A 62, 062314 (2000)

    Article  ADS  MathSciNet  Google Scholar 

  62. Acin A., BruX D., Lewenstein M., Sanpera A.: Classification of mixed three-qubit states. Phys. Rev. Lett. 87, 040401 (2001)

    Article  ADS  MathSciNet  Google Scholar 

  63. Joo, J., Lee, J., Jang, J., Park, Y.J.: Quantum secure communication with W states. eprint quantum-ph/0204003

  64. Guo G.C., Zhang Y.S.: Scheme for preparation of the W state via cavity quantum electrodynamics. Phys. Rev. A 65, 054302 (2002)

    Article  ADS  Google Scholar 

  65. Zou X.B., Pahlke K., Mathis W.: Generation of an entangled four-photon W state. Phys. Rev. A 66, 044302 (2001)

    Article  ADS  Google Scholar 

  66. Eibl E., Kiesel N., Bourennane M., Kurtsiefer C., Weinfurter H.: Experimental realization of a three-qubit entangled W state. Phys. Rev. Lett. 92, 077901 (2004)

    Article  ADS  Google Scholar 

  67. Wang X.: Entanglement in the quantum Heisenberg XY model. Phys. Rev. A 64, 012313 (2001)

    Article  ADS  Google Scholar 

  68. Zheng S.B.: Generation of entangled states of multiple trapped ions in thermal motion. Phys. Rev. A 70, 045804 (2004)

    Article  ADS  Google Scholar 

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  1. Key Laboratory of Optoelectronic Information Acquisition & Manipulation of Ministry of Education of China, School of Physics & Material Science, Anhui University, Hefei, 230039, China

    Zhang-yin Wang

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Wang, Zy. Classical communication cost and probabilistic remote two-qubit state preparation via POVM and W-type states. Quantum Inf Process 11, 1585–1602 (2012). https://doi.org/10.1007/s11128-011-0321-3

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