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Entanglement in General Multipartite Quantum Systems and Its Role in Quantum Information Processing Tasks

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Computer Networks (CN 2010)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 79))

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Abstract

A major role playing by entanglement of quantum states in several, present day applications of genuine quantum technologies is briefly reviewed. Additionally, the notion and classification of multipartite entanglement has been presented. A new, monotone under (S)LOCC-operations measures of many-partite entanglement are defined and discussed briefly.

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References

  1. Deutsch, D.: Quantum Theory the Church-Turing principle and the universal quantum computer. Proceed. R. Soc. 400, 97–117 (1985)

    Article  MATH  MathSciNet  Google Scholar 

  2. Feynman, R.P.: Keynote talk by R.P. Feynman, 1st Conference on Physics and Computations. MIT, Cambridge (1981); International Journal of Theoretical Physics 21, 467–488 (1982)

    Article  MathSciNet  Google Scholar 

  3. Shor, P.: Algorithms for quantum computations: discrete log and factoring. In: Goldwasser, S. (ed.) Proceedings of the 35th Annual Symposium on the Foundations of Computer Sciencem, pp. 124–134. IEEE Computer Society Press, Los Alamitos (1994)

    Chapter  Google Scholar 

  4. Petit, C.: Quantum Computer Simulates Hydrogen Molecule Just Right. Science News (January 2010)

    Google Scholar 

  5. DiCarlo, L.: Demonstration of two-qubit algorithms with a superconducting quantum processor. Nature 460, 240–244 (2009)

    Article  Google Scholar 

  6. Bennett, C.H., Bessette, F., Brassard, G., Salvail, L., Smolin, J.: Experimental Quantum Cryptology  5(1), 3–28 (1992)

    Google Scholar 

  7. Gisin, N., Ribordy, G., Tittel, W., Zbinden, H.: Quantum cryptography. Rev. Mod. Phys. 74, 145–194 (2002)

    Article  Google Scholar 

  8. Lo, H.-K., Lutkenhaus, L.: Quantum Cryptography: from theory to practise. Physics in Canada 63, 191 (2007)

    Google Scholar 

  9. Vaidman, L.: Teleportation of Quantum States. Phys. Rev. A 49, 1473–1476 (1994)

    Article  MathSciNet  Google Scholar 

  10. Peres, A.: What is actually teleported? IBM Journal of Research and Development 48(1)

    Google Scholar 

  11. Bugajski, S., Klamka, J., Wegrzyn, S.: Foundation of quantum computing. Part 1. Archiwum Informatyki Teoretycznej i Stosowanej 13(2), 97–142 (2001)

    Google Scholar 

  12. Bugajski, S., Klamka, J., Wegrzyn, S.: Foundation of quantum computing. Part 2. Archiwum Informatyki Teoretycznej i Stosowanej 14(2), 93–106 (2002)

    Google Scholar 

  13. Vernam, G.S.: Cipher printing telegraph systems for secrets wire and racho telegram communications. J.AIEE, 109 (1926)

    Google Scholar 

  14. Shannon, C.: Communication theory of secrecy systems. Bell System technical Journal 28(4), 656 (1949)

    MATH  MathSciNet  Google Scholar 

  15. Bennett, C.H., Brassard, G.: Quantum Cryptography: Public key distribution and coin tessing. In: Proc. IEEE Computer Systemsand Signal Processing, pp. 175–179. IEEE, Bangalore (1984)

    Google Scholar 

  16. Bennett, C.H.: Quantum cryptography using any two nonorthogonal states. Phys. Rev. Lett. 68, 3121 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  17. Lo, H.-K., Chau, H.-F.: Unconditional security of quantum key distribution over arbitrary long distances. Science 283, 2050

    Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  19. Acin, A., Gisin, N., Masanes, L.: From Bell theorem to secure QKD. Phys. Rev. Lett. 97, 120405 (2006)

    Article  Google Scholar 

  20. Bell, J.S.: Speakable and unspeakable in quantum mechanics. Cambridge University Press, Cambridge (1987)

    Google Scholar 

  21. Brassard, G., Salvail, L.: Secret key reconcilation by public discussion. In: Helleseth, T. (ed.) EUROCRYPT 1993. LNCS, vol. 765, pp. 410–423. Springer, Heidelberg (1994)

    Google Scholar 

  22. Mesanes, L., Winter, A.: Unconditional security of key distribution from causality constrains. http://arxiv.quant/ph/06066048 (2006)

  23. Ursin, R.: + 17 coauthors: Entanglement based quantum communication over 144 km. Nature 3, 481 (2007)

    Google Scholar 

  24. New Jornal of Physics 8, 193 (2006)

    Google Scholar 

  25. Schmitt-Manderbach et al.: Experimental demonstration of the free space decoy-state quantum key distribution over 144 km. Phys. rev. lett. 98, 1010504 (2007)

    Google Scholar 

  26. http://news.bbc.co.uk/1/hi/sci/tech/7661311.stm

  27. Dixon, A.R., Yuan, Z.L., Dynes, J.F., Sharpe, A.E., Shields, A.J.: Optics Express 16(23), 18790–18979

    Google Scholar 

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

    MATH  Google Scholar 

  29. Bennett, C.H., et al.: Teleporting an Unknown Quantum State via Dual Classical and Einstein-Podolsky-Rosen Channels. Phys. Rev. Lett. 70, 1895–1899 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  30. Werner, R.F.: All teleportation and Dense coding schemes, http://arXiv.quant/ph/003070v1

  31. Barrett, M.D., et al.: Deterministic Quantum Teleportation of Atomic Qubits. Nature 429, 737 (2004)

    Article  Google Scholar 

  32. Riebe, M., et al.: Deterministic Quantum Teleportation with Atoms. Nature 429, 734–737 (2004)

    Article  Google Scholar 

  33. Bengtsson, I., Życzkowski, K.: Geometry of Quantum States: An Introduction to Quantum Entanglement. Cambridge University Press, Cambridge (2006)

    Book  MATH  Google Scholar 

  34. Horodecki, R., Horodecki, P., Horodecki, M., Horodecki, K.: Quantum entanglement. Rev. Mod. Phys (2007), http://arxiv.org/abs/quant-ph/0702225

  35. Gurvits, L.: Classical deterministic complexity of Edmonds’ Problem and quantum entanglement. In: Proceedings of the thirty-fifth annual ACM symposium on Theory of computing (October 2003)

    Google Scholar 

  36. Gruska, J.: Quantum Computing. McGraw-Hill, New York (1999)

    Google Scholar 

  37. Gielerak, R., Sawerwain, M.: Twopartite, combinatorial approach to partial k-separability problem for general multipartite states, http://arXiv.quant/ph/1003.0103v1

  38. Plenio, M.B., Virmani, S.: An introduction to entanglement measures. Quant. Inf. Comp. 7, 1 (2007)

    Google Scholar 

  39. Sawerwain, M., Gielerak, R.: Natural quantum operational semantics with predicates. Int. J. Appl. Math. Comput. Sci. 18(3), 341–359 (2008)

    Google Scholar 

  40. Jaeger, G.: Entanglement, Information and the Interpretation of Quantum Mechanics. Springer, Heidelberg (2009)

    Book  Google Scholar 

  41. Bouwmeester, D., Pan, J.W., Mattle, K., Eibl, M., Weinfurter, H., Zeilinger, A.: Experimental Quantum Teleportation. Nature 390(6660), 575–579 (1997)

    Article  Google Scholar 

  42. Boschi, D., et al.: Experimental Realization of Teleporting an Unknown Pure Quantum State via Dual classical and Einstein-Podolsky-Rosen channels. Phys. Rev. Lett. 80(6), 1121–1125 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  43. Marcikic, I., et al.: Long-Distance Teleportation of Qubits at Telecommunication Wavelengths. Nature 421, 509 (2003)

    Article  Google Scholar 

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Gielerak, R. (2010). Entanglement in General Multipartite Quantum Systems and Its Role in Quantum Information Processing Tasks. In: Kwiecień, A., Gaj, P., Stera, P. (eds) Computer Networks. CN 2010. Communications in Computer and Information Science, vol 79. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13861-4_2

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  • DOI: https://doi.org/10.1007/978-3-642-13861-4_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-13860-7

  • Online ISBN: 978-3-642-13861-4

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