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Superposition of Entangled Coherent States: Physical Realization and Properties

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Abstract

Continuous variable entangled states and especially entangled coherent states have attracted increasing interest in the Geld of quantum information processing. The characteristic features of the superposition of quantum states can be found in the literature. Because of these significant findings, we introduce and investigate a special superposition of multipartite entangled coherent states. We prove that the free-traveling optical field scheme can generate such a superposed state. Using a geometric measure of entanglement, we then investigate the correlation behavior of the superposed state.

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References

  1. D. M. Greenberger, M. Home, and A. Zeilinger, “Going beyond Bell’s theorem,” in: Bell’s Theorem, Quantum Theory, and Conceptions of the Universe (Fund. Theor. Phys., Vol. 37. M. Kafatos, ed.), Kluwer, Dordrecht (1989), pp. 69–72.

    Google Scholar 

  2. W. Dur, G. Vidal, and J. I. Cirac, “Three qubits can be entangled in two inequivalent ways,” Phys. Rev. A, 62, 062314 (2000); arXiv:quant-ph/0005115v2 (2000).

    Article  ADS  MathSciNet  Google Scholar 

  3. R. Raussendorf and H. J. Briegel, “A one-way quantum computer,” Phys. Rev. Lett., 86, 5188–5191 (2001).

    Article  ADS  Google Scholar 

  4. R. H. Dicke, “Coherence in spontaneous radiation processes,” Phys. Rev., 93, 99–110 (1954).

    Article  ADS  MATH  Google Scholar 

  5. X. Wang and B. C. Sanders, “Multipartite entangled coherent states,” Phys. Rev. A, 65, 012303 (2001): arXiv:quant-ph/0104011v2 (2001).

    Article  ADS  MathSciNet  Google Scholar 

  6. N. B. An, “Optimal processing of quantum information via W-type entangled coherent states,” Phys. Rev. A, 69, 022315 (2004).

    Article  ADS  Google Scholar 

  7. P. P. Munhoz, F. L. Semiao, A. Vidiella-Barranco, and J. A. Roversi, “Cluster-type entangled coherent states,” Phys. Lett. A, 372, 3580–3585 (2008); arXiv:0705.1549v3 [quant-ph] (2007).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  8. E. M. Becerra-Castro, W. B. Cardoso, A. T. Avelar, and B. Baseia, “Generation of a 4-qubit cluster of entangled coherent states in bimodal QED cavities,” J. Phys. B, 41, 085505 (2008); arXiv:0709.0010v2 [quant-ph] (2007).

    Article  ADS  Google Scholar 

  9. N. B. An and J. Kim, “Cluster-type entangled coherent states: generation and application,” Phys. Rev. A, 80, 042316 (2009).

    Article  ADS  Google Scholar 

  10. X. Wang, “Quantum teleportation of entangled coherent states,” Phys. Rev. A, 64, 022302 (2001); arXiv:quant-ph/0102048v2 (2001).

    Article  ADS  MathSciNet  Google Scholar 

  11. H. Jeong and M. S. Kim, “Efficient quantum computation using coherent states,” Phys. Rev. A, 65, 042305 (2002); arXiv:quant-ph/0109077v2 (2001).

    Article  ADS  Google Scholar 

  12. N. B. An, “Teleportation of coherent-state superpositions within a network,” Phys. Rev. A, 68, 022321 (2003).

    Article  ADS  Google Scholar 

  13. H. Prakash, N. Chandra, R. Prakash, and Shivani, “Improving the teleportation of entangled coherent states,” Phys. Rev. A, 75, 044305 (2007).

    Article  ADS  Google Scholar 

  14. A. M. Lance, T. Symul, W. P. Bowen, B. C. Sanders, and P. K. Lam, “Tripartite quantum state sharing,” Phys. Rev. Lett., 92, 177903 (2004); arXiv:quant-ph/0311015v2 (2003).

    Article  ADS  Google Scholar 

  15. O. Abbasi and M. K. Tavassoly, “Superposition of two nonlinear coherent states out of phase and their nonclassical properties,” Opt. Commun., 282, 3737–3745 (2009); arXiv:0907.0083vl [quant-ph] (2009).

    Article  ADS  Google Scholar 

  16. M. C. de Oliveira and W. J. Munro, “Quantum computation with mesoscopic superposition states,” Phys. Rev. A, 61, 042309 (2000); arXiv:quant-ph/0001018vl (2000).

    Article  ADS  Google Scholar 

  17. S. J. van Enk and O. Hirota, “Entangled coherent states: Teleportation and decoherence,” Phys. Rev. A, 64, 022313 (2001); arXiv:quant-ph/0012086vl (2000).

    Article  ADS  Google Scholar 

  18. T. C. Ralph, A. Gilchrist, G. J. Milburn, W. J. Munro, and S. Glancy, “Quantum computation with optical coherent states,” Phys. Rev. A, 68, 042319 (2003); arXiv:quant-ph/0306004vl (2003).

    Article  ADS  Google Scholar 

  19. P. Marek and J. Fiurasek, “Elementary gates for quantum information with superposed coherent states,” Phys. Rev. A, 82, 014304 (2010); arXiv:1006.3644v2 [quant-ph] (2010).

    Article  ADS  Google Scholar 

  20. S. L. Braunstein and H. J. Kimble, “Dense coding for continuous variables,” Phys. Rev. A, 61, 042302 (2000); arXiv:quant-ph/9910010vl (1999).

    Article  ADS  MathSciNet  Google Scholar 

  21. D. Das, S. Dogra, K. Dorai, and Arvind, “Experimental construction of a W superposition state and its equivalence to the Greenberger-Horne-Zeilinger state under local filtration,” Phys. Rev. A, 92, 022307 (2015); arXiv:1504.04856vl [quant-ph] (2015).

    Article  ADS  Google Scholar 

  22. A. R. Usha Devi, Sudha, and A. K. Rajagopal, “Majorana representation of symmetric multiqubit states,” Quant. Inf. Process, 11, 685–710 (2012).

    Article  MathSciNet  MATH  Google Scholar 

  23. F. Ozaydin, A. A. Altintas, S. Bugu, and C. Yesilyurt, “Quantum Fisher information of N particles in the superposition of W and GHZ states,” Internat. J. Theor. Phys., 52, 2977–2980 (2013).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  24. L. Tang and F. Liu, “Generation of multipartite entangled coherent states via a superconducting charge qubit,” Phys. Lett. A, 378, 2074–2078 (2014).

    Article  ADS  MATH  Google Scholar 

  25. N. Behzadi, B. Ahansaz, and S. Kazemi, “Constructing robust entangled coherent GHZ and W states via a cavity QED system,” Internat. J. Theor. Phys., 55, 1577–1592 (2016).

    Article  ADS  MATH  Google Scholar 

  26. L.-M. Kuang and L. Zhou, “Generation of atom-photon entangled states in atomic Bose-Einstein condensate via electromagnetically induced transparency,” Phys. Rev. A, 68, 043606 (2003); arXiv:quant-ph/0402031vl (2004).

    Article  ADS  Google Scholar 

  27. L.-M. Kuang, Z.-B. Chen, and J.-W. Pan, “Generation of entangled coherent states for distant Bose-Einstein condensates via electromagnetically induced transparency,” Phys. Rev. A, 76, 052324 (2007); arXiv:0903.1210vl [quant-ph] (2009).

    Article  ADS  Google Scholar 

  28. H. Jeong and N. B. An, “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); arXiv:quant-ph/0606109v2 (2006).

    Article  ADS  MathSciNet  Google Scholar 

  29. Y. Guo and L.-M. Kuang, “Near-deterministic generation of four-mode TF-type entangled coherent states,” J. Phys. B, 40, 3309–3318 (2007).

    Article  ADS  Google Scholar 

  30. Y. Guo and L.-M. Kuang, “Generation of three-mode W-type entangled coherent states in free-travelling optical fields,” Chinese Opt. Lett., 6, 303–306 (2008).

    Article  Google Scholar 

  31. H. Ollivier and W. H. Zurek, “Quantum discord: A measure of the quantumness of correlations,” Phys. Rev. Lett., 88, 017901 (2001); arXiv:quant-ph/0105072v3 (2001).

    Article  ADS  MATH  Google Scholar 

  32. S. Luo and S. Fu, “Measurement-induced nonlocality,” Phys. Rev. Lett., 106, 120401 (2011).

    Article  ADS  MATH  Google Scholar 

  33. R. Hubener, M. Kleinmann, T.-C. Wei, C. Gonzalez-Guillen, and O. Guhne, “Geometric measure of entanglement for symmetric states,” Phys. Rev. A, 80, 032324 (2009); arXiv:0905.4822v2 [quant-ph] (2009).

    Article  ADS  MathSciNet  Google Scholar 

  34. J. Claudon, J. Bleuse, N. S. Malik, M. Bazin, P. Jaffrennou, N. Gregersen, C. Sauvan, P. Lalanne, and J.-M. Gérard, “A highly efficient single-photon source based on a quantum dot in a photonic nanowire,” Nature Photonics, 4, 174–177 (2010).

    Article  ADS  Google Scholar 

  35. C. C. Gerry and P. Knight, Introductory Quantum Optics, Cambridge Univ. Press, Cambridge (2005).

    Google Scholar 

  36. T. Peyronel, O. Firstenberg, Q.-Y. Liang, S. Hofferberth, A. V. Gorshkov, T. Pohl, M. D. Lukin, and V. Vuletic, “Quantum nonlinear optics with single photons enabled by strongly interacting atoms,” Nature, 488, 57–60 (2012).

    Article  ADS  Google Scholar 

  37. J. Stanojevic, V. Parigi, E. Bimbard, A. Ourjoumtsev, and P. Grangier, “Dispersive optical nonlinearities in a Rydberg electromagnetically-induced-transparency medium,” Phys. Rev. A, 88, 053845 (2013).

    Article  ADS  Google Scholar 

  38. O. Firstenberg, T. Peyronel, Q.-Y. Liang, A. V. Gorshkov, M. D. Lukin, and V. Vuletic, “Attractive photons in a quantum nonlinear medium,” Nature, 502, 71–75 (2013).

    Article  ADS  Google Scholar 

  39. Z. Bai and G. Huang, “Enhanced third-order and fifth-order Kerr nonlinearities in a cold atomic system via Rydberg-Rydberg interaction,” Opt. Express, 24, 4442–4461 (2016); arXiv:1604.00585vl [physics.optics] (2016).

    Article  ADS  Google Scholar 

  40. L. S. Costanzo, A. S. Coelho, N. Biagi, J. Fiuášek, M. Bellini, and A. Zavatta, “Measurement-induced strong Kerr nonlinearity for weak quantum states of light,” Phys. Rev. Lett., 119, 013601 (2017); arXiv:1706.07018vl [quant-ph] (2017).

    Article  ADS  Google Scholar 

  41. H. Qian, Y. Xiao, and Z. Liu, “Giant Kerr response of ultrathin gold films from quantum size effect,” Nature Commun., 7, 13153 (2016).

    Article  ADS  Google Scholar 

  42. M. M. Müller, A. Kölle, R. Löw, T. Pfau, T. Calarco, and S. Montangero, “Room-temperature Rydberg single-photon source,” Phys. Rev. A, 87, 053412 (2013); arXiv:1212.2811vl [quant-ph] (2012).

    Article  ADS  Google Scholar 

  43. M. Khazali, K. Heshami, and C. Simon, “Single-photon source based on Rydberg exciton blockade,” J. Phys. B, 50, 215301 (2017); arXiv:1702.01213vl [quant-ph] (2017).

    Article  ADS  Google Scholar 

  44. P. Parashar and S. Rana, “Entanglement and discord of the superposition of Greenberger-Horne-Zeilinger states,” Phys. Rev. A, 83, 032301 (2011).

    Article  ADS  Google Scholar 

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Acknowledgments

The author expresses utmost thanks to Professors S. J. Akhtarshenas and M. K. Tavassoly for their helpful comments and suggestions, which substantially improved the contents of the paper.

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  1. Department of Engineering Sciences and Physics, Buein Zahra Technical University, Buein Zahra, Qazvin, Iran

    S. R. Miry

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Correspondence to S. R. Miry.

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Prepared from an English manuscript submitted by the author; for the Russian version, see Teoreticheskaya i Matematicheskaya Fizika, Vol. 200, No. 1, pp. 96–105, July, 2019.

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Miry, S.R. Superposition of Entangled Coherent States: Physical Realization and Properties. Theor Math Phys 200, 1006–1014 (2019). https://doi.org/10.1134/S0040577919070055

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