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Synchronous concentration and purification schemes of arbitrary unknown hyperentangled mixed states

  • DU Kun ,
  • SONG Qiucheng ,
  • QIAO Congfeng
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  • University of Chinese Academy of Sciences, Beijing 100049, China

Received date: 2014-05-07

  Revised date: 2014-05-13

  Online published: 2015-03-15

Supported by

Supported by National Natural Science Foundation of China(NSFC)(11175249, 11375200)

Abstract

We present two efficient schemes which can simultaneously accomplish hyperentanglement concentration and purification for two-photon four-qubit systems in an unknown partially hyperentangled mixed state. The first can correct errors in the polarization entanglement and extract maximal hyperentanglement in polarization and spatial mode, using additional partial frequency entanglement. The second uses additional maximal frequency entanglement to purify and concentrate hyperentanglement in polarization and spatial mode deterministically. Both of the schemes are only based on existing optical devices and cross-Kerr nonlinearities.

Cite this article

DU Kun , SONG Qiucheng , QIAO Congfeng . Synchronous concentration and purification schemes of arbitrary unknown hyperentangled mixed states[J]. Journal of University of Chinese Academy of Sciences, 2015 , 32(2) : 158 -165 . DOI: 10.7523/j.issn.2095-6134.2015.02.003

References

[1] Raussendorf R, Briegel H J. A one-way quantum computer[J]. PRL, 2001,86:5 188-5 191.

[2] Bennett C H, Brassard G, Crépeau C, et al. Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels[J]. PRL, 1993, 70:1 895.

[3] Wang C, Deng F G, Li Y S, et al. Quantum secure direct communication with high-dimension quantum superdense coding[J]. PRA, 2005, 71:044 305.

[4] Bruss D, Macchiavello C. Optimal eavesdropping in cryptography with three-dimensional quantum states[J]. PRL, 2002,88:127 901.

[5] Gisin N, Ribordy G, Tittel W, et al. Quantum cryptography[J]. RMP, 2002,74:145.

[6] Kwiat P G. Hyper-entangled states[J]. JMO, 1997, 44:2 173-2 184.

[7] Kwiat P G, Waks E, White A G, et al. Ultrabright source of polarization-entangled photons[J]. PRA, 1999,60:R773.

[8] Barbieri M, Cinelli C, Mataloni P, et al. Polarization-momentum hyperentangled states: Realization and characterization[J]. PRA, 2005,72: 052 110.

[9] Xu H B, Du K, Qiao C F. Proposal for a new scheme for producing a two-photon, high dimensional hyperentangled state[J]. JMO, 2012, 59:1 265–1 271.

[10] Walborn S P,Nogueira W A T, Padua S, et al. Optical Bell-state analysis in the coincidence basis[J]. EPL, 2003, 62:161.

[11] Schuck C, Huber G, Kurtsiefer C, et al. Complete deterministic linear optics bell state analysis[J]. PRL, 2006,96:190 501.

[12] Barbieri M, Vallone G, Mataloni P, et al. Complete and deterministic discrimination of polarization Bell states assisted by momentum entanglement[J]. PRA, 2007, 75: 042 317.

[13] Simon C, Pan J W. Polarization entanglement purification using spatial entanglement[J]. PRL, 2002,89:257 901.

[14] Bennett CH, Brassard G, Popescu S, et al. Purification of noisy entanglement and faithful teleportation via noisy channels[J]. PRL, 1996,76:722.

[15] Pan J W, Gasparonl S, Ursin R, et al. Experimental entanglement purification of arbitrary unknown states[J]. Nature, 2003, 423:417.

[16] Wang T J, Song S Y, Long G L. Quantum repeater based on spatial entanglement of photons and quantum-dot spins in optical microcavities[J]. PRA, 2012, 85: 062 311.

[17] Bennett C H, Bernstein H J, Popescu S, et al. Concentrating partial entanglement by local operations[J]. PRA, 1996, 53: 2 046.

[18] Simon C, Pan J W. Polarization entanglement purification using spatial entanglement[J]. PRL, 2002,89:257 901.

[19] Sheng Y B, Deng F G. One-step deterministic polarization-entanglement purification using spatial entanglement[J]. PRA, 2010,82:044 305.

[20] Sheng Y B, Zhou L, Long G L. Hybrid entanglement purification for quantum repeaters[J]. PRA, 2013,88:022 302.

[21] Deng F G. Optimal nonlocal multipartite entanglement concentration based on projection measurements[J]. PRA, 2012, 85:022 311.

[22] Zhao Z, Pan J W, Zhan M S. Practical scheme for entanglement concentration[J]. PRA, 2001,64:014 301.

[23] Ren B C, Du F F, Deng F G. Hyperentanglement concentration for two-photon four-qubit systems with linear optics[J]. PRA, 2013,88:012 302.

[24] Ren B C, Deng F G. Hyperentanglement purification and concentration assisted by diamond NV centers inside photonic crystal cavities[J]. LPL, 2013,10:115 201.

[25] Ren B C, Long G L. General hyperentanglement concentration for photon systems assisted by quantum-dot spins inside optical microcavities[J]. Optics Express, 2014,22:6 547-6 561.

[26] Sheng Y B, Deng F G. Deterministic entanglement purification and complete nonlocal Bell-state analysis with hyperentanglement[J]. PRA, 2010,81:032 307.

[27] Bruss D. Optimal eavesdropping in quantum cryptography with six states[J]. PRL, 1998,81:3 018.

[28] Bechmann-Pasquinucci H, Gisin N. Incoherent and coherent eavesdropping in the six-state protocol of quantum cryptography[J]. PRA, 1999,59:4 238.

[29] Merolla J M, Mazurenko Y, Goedgebuer J P, et al. Single-photon interference in sidebands of phase-modulated light for quantum cryptography[J]. PRL, 1999,82:1 656.

[30] Minár J, Riedmatten H D, Simon C, et al. Phase-noise measurements in long-fiber interferometers for quantum-repeater applications[J]. PRA, 2008, 77:052 325.

[31] Sheng Y B, Deng F G, Zhou H Y. Efficient polarization-entanglement purification based on parametric down-conversion sources with cross-Kerr nonlinearity[J]. PRA, 2008, 77:042 308.

[32] Sheng Y B, Deng F G, Long G L. Complete hyperentangled-Bell-state analysis for quantum communication[J]. PRA, 2010,82:032 318.

[33] He B, Ren Y H, Bergou J A. Creation of high-quality long-distance entanglement with flexible resources[J]. PRA, 2009,79:052 323.

[34] Nemoto K, Munro W J. Nearly deterministic linear optical controlled-NOT gate[J]. PRL, 2004, 250 502.

[35] Barrett S D, Kok P, Nemoto K, et al. A symmetry analyzer for non-destructive Bell state detection using EIT[J]. PRA, 2005,71:060 302.

[36] Lin Q, He B, Bergou J A, et al. Processing multi-photon state through operation on single photon: methods and applications[J]. Phys Rev A, 2009,80:042 311.

[37] Shapiro J H. Single-photon Kerr nonlinearities do not help quantum computation[J]. PRA, 2006,73:062 305.

[38] Shapiro J H, Razavi M. Continuous-time cross-phase modulation and quantum computation[J]. New Journal of Physics, 2007, 9:16.

[39] Lukin M D, Imamo lu A. Nonlinear Optics and Quantum Entanglement of Ultraslow Single Photons[J]. PRL, 2000,84:1 419.

[40] Petrosyan D, Kurizki G. Symmetric photon-photon coupling by atoms with Zeeman-split sublevels[J]. PRA, 2002,65:033 833.

[41] Munro W J, Nemoto K, Spiller T P. Weak nonlinearities: a new route to optical quantum computation[J]. New Journal of Physics, 2005,7:137.

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