## Effective protocol for preparation of four-photon polarization-entangled decoherence-free states with cross-Kerr nonlinearity |

JOSA B, Vol. 30, Issue 2, pp. 421-427 (2013)

http://dx.doi.org/10.1364/JOSAB.30.000421

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### Abstract

We propose an effective protocol for preparation of four-photon polarization-entangled decoherence-free states with quantum nondemolition detectors. The protocol is based on optical elements, single polarization photons, and cross-Kerr nonlinearity, which are feasible with existing experimental technology. Compared with previous protocols, the present one is to replace the entangled-state resources with much simpler single-photon resources and has a higher success probability. All these advantages make this protocol more efficient and more convenient than others in the applications in quantum communication.

© 2013 Optical Society of America

**OCIS Codes**

(000.6800) General : Theoretical physics

(270.5565) Quantum optics : Quantum communications

(270.5585) Quantum optics : Quantum information and processing

**ToC Category:**

Quantum Optics

**History**

Original Manuscript: December 3, 2012

Revised Manuscript: December 15, 2012

Manuscript Accepted: December 15, 2012

Published: January 22, 2013

**Citation**

Yan Xia, Mei Lu, Jie Song, Pei-Min Lu, and He-Shan Song, "Effective protocol for preparation of four-photon polarization-entangled decoherence-free states with cross-Kerr nonlinearity," J. Opt. Soc. Am. B **30**, 421-427 (2013)

http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-30-2-421

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### References

- A. Einstein, B. Podolsky, and N. Rosen, “Can quantum-mechanical description of physical reality be considered complete?” Phys. Rev. 47, 777–780 (1935). [CrossRef]
- J. S. Bell, “On the Einstein–Podolsky–Rosen paradox,” Physics 1, 195–200 (1964).
- A. K. Ekert, “Quantum cryptography based on Bell’s theorem,” Phys. Rev. Lett. 67, 661–663 (1991). [CrossRef]
- N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145–195 (2002). [CrossRef]
- C. H. Bennett and S. J. Wiesner, “Communication via one- and two-particle operators on Einstein–Podolsky–Rosen states,” Phys. Rev. Lett. 69, 2881–2884 (1992). [CrossRef]
- C. H. Bennett, G. Brassard, C. Crepeau, R. Jozsa, A. Peres, and W. K. Wootters, “Teleporting an unknown quantum state via dual classical and Einstein–Podolsky–Rosen channels,” Phys. Rev. Lett. 70, 1895–1899 (1993). [CrossRef]
- C. Wang, L. Xiao, W. Y. Wang, G. Y. Zhang, and G. L. Long, “Quantum key distribution using polarization and frequency hyperentangled photons,” J. Opt. Soc. Am. B 26, 2072–2076 (2009). [CrossRef]
- G. L. Long and X. S. Liu, “Theoretically efficient high-capacity quantum-key-distribution scheme,” Phys. Rev. A 65, 032302 (2002). [CrossRef]
- F. G. Deng and G. L. Long, “Two-step quantum direct communication protocol using the Einstein–Podolsky–Rosen pair block,” Phys. Rev. A 68, 042317 (2003). [CrossRef]
- H. Kim, Y. M. Cheong, and H. W. Lee, “Generalized measurement and conclusive teleportation with nonmaximal entanglement,” Phys. Rev. A 70, 012309 (2004). [CrossRef]
- P. W. Shor, “Scheme for reducing decoherence in quantum computer memory,” Phys. Rev. A 52, R2493 (1995). [CrossRef]
- A. M. Steane, “Error correcting codes in quantum theory,” Phys. Rev. Lett. 77, 793–797 (1996). [CrossRef]
- R. Laflamme, C. Miquel, J. P. Paz, and W. H. Zurek, “Perfect quantum error correcting code,” Phys. Rev. Lett. 77, 198–201(1996). [CrossRef]
- Z. D. Walton, A. F. Abouraddy, A. V. Sergienko, B. E. A. Saleh, and M. C. Teich, “Decoherence-free subspaces in quantum key distribution,” Phys. Rev. Lett. 91, 087901 (2003). [CrossRef]
- T. Yamamoto, J. Shimamura, S. K. Özdemir, M. Koashi, and N. Imoto, “Faithful qubit distribution assisted by one additional qubit against collective noise,” Phys. Rev. Lett. 95, 040503 (2005). [CrossRef]
- D. Kalamidas, “Single-photon quantum error rejection and correction with linear optics,” Phys. Lett. A 343, 331–335 (2005). [CrossRef]
- X. H. Li, F. G. Deng, and H. Y. Zhou, “Faithful qubit transmission against collective noise without ancillary qubits,” Appl. Phys. Lett. 91, 144101 (2007). [CrossRef]
- Y. B. Sheng and F. G. Deng, “Efficient quantum entanglement distribution over an arbitrary collective-noise channel,” Phys. Rev. A 81, 042332 (2010). [CrossRef]
- L. Viola, E. Knill, and S. Lloyd, “Dynamical decoupling of open quantum systems,” Phys. Rev. Lett. 82, 2417–2421 (1999). [CrossRef]
- C. H. Bennett, H. J. Bernstein, S. Popescu, and B. Schumacher, “Concentrating partial entanglement by local operations,” Phys. Rev. A 53, 2046–2052 (1996). [CrossRef]
- S. Bose, V. Vedral, and P. L. Knight, “Purification via entanglement swapping and conserved entanglement,” Phys. Rev. A 60, 194–197 (1999). [CrossRef]
- B. S. Shi, Y. K. Jiang, and G. C. Guo, “Optimal entanglement purification via entanglement swapping,” Phys. Rev. A 62, 054301 (2000). [CrossRef]
- T. Yamamoto, M. Koashi, and N. Imoto, “Concentration and purification scheme for two partially entangled photon pairs,” Phys. Rev. A 64, 012304 (2001). [CrossRef]
- Z. Zhao, J. W. Pan, and M. S. Zhan, “Practical scheme for entanglement concentration,” Phys. Rev. A 64, 014301 (2001). [CrossRef]
- Y. B. Sheng, F. G. Deng, and H. Y. Zhou, “Nonlocal entanglement concentration scheme for partially entangled multipartite systems with nonlinear optics,” Phys. Rev. A 77, 062325 (2008). [CrossRef]
- Y. B. Sheng, L. Zhou, S. M. Zhao, and B. Y. Zheng, “Efficient single-photon-assisted entanglement concentration for partially entangled photon pairs,” Phys. Rev. A 85, 012307 (2012). [CrossRef]
- Y. B. Sheng, L. Zhou, and S. M. Zhao, “Efficient two-step entanglement concentration for arbitrary W states,” Phys. Rev. A 85, 042302 (2012). [CrossRef]
- F. G. Deng, “Optimal nonlocal multipartite entanglement concentration based on projection measurements,” Phys. Rev. A 85, 022311 (2012). [CrossRef]
- Z. Zhao, T. Yang, Y. A. Chen, A. N. Zhang, and J. W. Pan, “Experimental realization of entanglement concentration and a quantum repeater,” Phys. Rev. Lett. 90, 207901 (2003). [CrossRef]
- T. Yamamoto, M. Koashi, S. K. Ozdemir, and N. Imoto, “Experimental extraction of an entangled photon pair from two identically decohered pairs,” Nature 421, 343–346 (2003). [CrossRef]
- C. H. Bennett, G. Brassard, S. Popescu, B. Schumacher, J. A. Smolin, and W. K. Wootters, “Purification of noisy entanglement and faithful teleportation via noisy channels,” Phys. Rev. Lett. 76, 722–725 (1996). [CrossRef]
- D. Deutsch, A. Ekert, R. Jozsa, C. Macchiavello, S. Popescu, and A. Sanpera, “Quantum privacy amplification and the security of quantum cryptography over noisy channels,” Phys. Rev. Lett. 77, 2818–2821 (1996). [CrossRef]
- J. W. Pan, C. Simon, C. Brukner, and A. Zellinger, “Entanglement purification for quantum communication,” Nature 410, 1067–1070 (2001). [CrossRef]
- C. Simon and J. W. Pan, “Polarization entanglement purification using spatial entanglement,” Phys. Rev. Lett. 89, 257901 (2002). [CrossRef]
- Y. B. Sheng, F. G. Deng, and H. Y. Zhou, “Efficient polarization-entanglement purification based on parametric down-conversion sources with cross-Kerr nonlinearity,” Phys. Rev. A 77, 042308 (2008). [CrossRef]
- X. H. Li, “Deterministic polarization-entanglement purification using spatial entanglement,” Phys. Rev. A 82, 044304 (2010). [CrossRef]
- Y. B. Sheng and F. G. Deng, “Deterministic entanglement purification and complete nonlocal Bell-state analysis with hyperentanglement,” Phys. Rev. A 81, 032307 (2010). [CrossRef]
- F. G. Deng, “One-step error correction for multipartite polarization entanglement,” Phys. Rev. A 83, 062316 (2011). [CrossRef]
- C. Wang, Y. Zhang, and G. S. Jin, “Entanglement purification and concentration of electron-spin entangled states using quantum-dot spins in optical microcavities,” Phys. Rev. A 84, 032307 (2011). [CrossRef]
- C. Wang, Y. Zhang, and G. S. Jin, “Polarization-entanglement purification and concentration using cross-Kerr nonlinearity,” Quantum Inf. Comput. 11, 988–1002 (2011).
- F. G. Deng, “Efficient multipartite entanglement purification with the entanglement link from a subspace,” Phys. Rev. A 84, 052312 (2011). [CrossRef]
- C. Wang, Y. B. Sheng, X. H. Li, F. G. Deng, W. Zhang, and G. L. Long, “Efficient entanglement purification for doubly entangled photon state,” Sci. China Ser. E 52, 3464–3467 (2009). [CrossRef]
- L. M. Duan and G. C. Guo, “Preserving coherence in quantum computation by pairing quantum bits,” Phys. Rev. Lett. 79, 1953–1956 (1997). [CrossRef]
- J. Kempe, D. Bacon, D. A. Lidar, and K. B. Whaley, “Theory of decoherence-free fault-tolerant universal quantum computation,” Phys. Rev. A 63, 042307 (2001). [CrossRef]
- J. B. Altepeter, P. G. Hadley, S. M. Wendelken, A. J. Berglund, and P. G. Kwiat, “Experimental investigation of a two-qubit decoherence-free subspace,” Phys. Rev. Lett. 92, 147901 (2004). [CrossRef]
- M. Bourennane, M. Eibl, S. Gaertner, C. Kurtsiefer, A. Cabello, and H. Weinfurter, “Decoherence-free quantum information processing with four-photon entangled states,” Phys. Rev. Lett. 92, 107901 (2004). [CrossRef]
- X. B. Zou, J. Shu, and G. C. Guo, “Simple scheme for generating four-photon polarization-entangled decoherence-free states using spontaneous parametric down-conversions,” Phys. Rev. A 73, 054301 (2006). [CrossRef]
- Y. X. Gong, X. B. Zou, X. L. Niu, J. Li, Y. F. Huang, and G. C. Guo, “Generation of arbitrary four-photon polarization-entangled decoherence-free states,” Phys. Rev. A 77, 042317 (2008). [CrossRef]
- Y. Xia, J. Song, H. S. Song, and S. Zhang, “Controlled generation of four-photon polarization-entangled decoherence-free states with conventional photon detectors,” J. Opt. Soc. Am. B 26, 129–132 (2009). [CrossRef]
- Y. Xia, J. Song, Z. B. Yang, and S. B. zheng, “Generation of four-photon polarization-entangled decoherence-free states within a network,” Appl. Phys. B 99, 651–656 (2010). [CrossRef]
- Y. Xia, J. Song, P. M. Lu, and H. S. Song, “Generation of four-atom entangled decoherence-free states by interference of polarized photons,” J. Mod. Opt. 56, 1545–1549 (2009). [CrossRef]
- K. Nemoto and W. J. Munro, “Nearly deterministic linear optical controlled-NOT gate,” Phys. Rev. Lett. 93, 250502 (2004). [CrossRef]
- Y. Xia, J. Song, P. M. Lu, and H. S. Song, “Efficient implementation of the two-qubit controlled phase gate with cross-Kerr nonlinearity,” J. Phys. B 44, 025503 (2011). [CrossRef]
- Y. Xia, Q. Q. Chen, J. Song, and H. S. Song, “Efficient hyperentangled Greenberger–Horne–Zeilinger states analysis with cross-Kerr nonlinearity,” J. Opt. Soc. Am. B 29, 1029–1037 (2012). [CrossRef]
- Y. B. Sheng, F. G. Deng, and G. L. Long, “Complete hyperentangled-Bell-state analysis for quantum communication,” Phys. Rev. A 82, 032318 (2010). [CrossRef]
- G. L. Long, “General quantum interference principle and duality computer,” Commun. Theor. Phys. 45, 825–844 (2006). [CrossRef]
- X. B. Zou, K. Pahike, and W. Mathis, “Generation of an entangled four-photon W state,” Phys. Rev. A 66, 044302 (2002). [CrossRef]
- P. Kok, W. J. Munro, K. Nemoto, T. C. Ralph, J. P. Dowing, and G. J. Milburn, “Linear optical quantum computing with photonic qubits,” Rev. Mod. Phys. 79, 135–174 (2007). [CrossRef]
- J. H. Shapiro, “Single-photon Kerr nonlinearities do not help quantum computation,” Phys. Rev. A 73, 062305 (2006). [CrossRef]
- J. H. Shapiro and M. Razavi, “Continuous-time cross-phase modulation and quantum computation,” New J. Phys. 9, 1–17 (2007). [CrossRef]
- S. D. Barrett, P. Kok, K. Nemoto, R. G. Beausoleil, W. J. Munro, and T. P. Spiller, “Symmetry analyzer for nondestructive Bell-state detection using weak nonlinearities,” Phys. Rev. A 71, 060302(R) (2005). [CrossRef]
- H. F. Hofmann, K. Kojima, S. Takeuchi, and K. Sasaki, “Optimized phase switching using a single-atom nonlinearity,” J. Opt. B Quantum Semiclass. Opt 5, 218–221 (2003). [CrossRef]
- P. Kok, “Effects of self-phase-modulation on weak nonlinear optical quantum gates,” Phys. Rev. A 77, 013808 (2008). [CrossRef]
- Q. Lin and B. He, “Single-photon logic gates using minimal resources,” Phys. Rev. A 80, 042310 (2009). [CrossRef]
- Q. Lin, B. He, J. A. Bergou, and Y. H. Ren, “Processing multiphoton states through operation on a single photon: methods and applications,” Phys. Rev. A 80, 042311 (2009). [CrossRef]
- H. Schmidt and A. Imamoglu, “Giant Kerr nonlinearities obtained by electromagnetically induced transparency,” Opt. Lett. 21, 1936–1938 (1996). [CrossRef]
- Y. Xia, J. Song, and H. S. Song, “Linear optical protocol for preparation of N-photon Greenberger–Horne–Zeilinger state with conventional photon detectors,” Appl. Phys. Lett. 92, 021127 (2008). [CrossRef]
- M. Eibl, N. Kiesel, M. Bourennane, C. Kurtsiefer, and H. Weinfurter, “Experimental realization of a three-qubit entangled W state,” Phys. Rev. Lett. 92, 077901 (2004). [CrossRef]
- J. W. Pan, D. Bouwmeester, M. Daniell, H. Weinfurter, and A. Zeilinger, “Experimental test of quantum nonlocality in three-photon Greenberger–Horne–Zeilinger entanglement,” Nature 403, 515–519 (2000). [CrossRef]
- D. Bouwmeester, J. W. Pan, M. Daniell, H. Weinfurter, and A. Zeilinger, “Observation of three-photon Greenberger–Horne–Zeilinger entanglement,” Phys. Rev. Lett. 82, 1345–1349 (1999). [CrossRef]

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