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Dimension Witnesses

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Temporal Quantum Correlations and Hidden Variable Models

Part of the book series: Springer Theses ((Springer Theses))

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Abstract

The recent progress in the experimental control and manipulation of physical systems at the quantum level opens new possibilities (e.g., quantum communication, computation, and simulation), but, at the same time, demands the development of novel theoretical tools of analysis. There are already tools which allow us to recognize quantum entanglement and certify the usefulness of quantum states for quantum information processing tasks [1, 2]. However, on a more fundamental level, there are still several problems which have to be addressed. For example, how can one efficiently test whether measurements actually access all the desired energy levels of an ion? How to certify that the different paths of photons in an interferometer can be used to simulate a given multi-dimensional quantum system? Similar questions arise in the analysis of experiments with orbital angular momentum, where high-dimensional entanglement can be produced [3, 4], or in experiments with electron spins at nitrogen-vacancy centers in diamond, where the quantumness of the measurements should be certified [5].

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References

  1. R. Horodecki, P. Horodecki, M. Horodecki, K. Horodecki, Rev. Mod. Phys. 81, 865 (2009). doi:10.1103/RevModPhys.81.865

    Article  ADS  Google Scholar 

  2. O. Gühne, G. Tóth, Phys. Rep. 474, 1 (2009). doi:10.1016/j.physrep.2009.02.004

    Article  ADS  MathSciNet  Google Scholar 

  3. G. Molina-Terriza, J.P. Torres, L. Torner, Nat. Phys. 3, 305 (2007). doi:10.1038/nphys607

    Article  Google Scholar 

  4. A.C. Dada, J. Leach, G.S. Buller, M.J. Padgett, E. Andersson, Nat. Phys. 7, 677 (2011). doi:10.1038/nphys1996

    Article  Google Scholar 

  5. P. Neumann, N. Mizuochi, F. Rempp, P. Hemmer, H. Watanabe, S. Yamasaki, V. Jacques, T. Gaebel, F. Jelezko, J. Wrachtrup, Science 320, 1326 (2008). doi:10.1126/science.1157233

    Article  ADS  Google Scholar 

  6. N. Brunner, S. Pironio, A. Acín, N. Gisin, A. Méthot, V. Scarani, Phys. Rev. Lett. 100, 210503 (2008). doi:10.1103/PhysRevLett.100.210503

    Article  ADS  MathSciNet  Google Scholar 

  7. T. Vértesi, K.F. Pál, Phys. Rev. A 79, 042106 (2009). doi:10.1103/PhysRevA.79.042106

    Article  ADS  Google Scholar 

  8. S. Wehner, M. Christandl, A.C. Doherty, Phys. Rev. A 78, 062112 (2008). doi:10.1103/PhysRevA.78.062112

    Article  ADS  Google Scholar 

  9. R. Gallego, N. Brunner, C. Hadley, A. Acín, Phys. Rev. Lett. 105, 230501 (2010). doi:10.1103/PhysRevLett.105.230501

    Article  ADS  Google Scholar 

  10. N. Brunner, M. Navascus, T. Vrtesi, Phys. Rev. Lett. 110, 150501 (2013). doi:10.1103/PhysRevLett.110.150501

    Article  ADS  Google Scholar 

  11. M. Hendrych, R. Gallego, M. Mičuda, N. Brunner, A. Acín, J.P. Torres, Nat. Phys. 8, 588 (2012). doi:10.1038/nphys2334

    Article  Google Scholar 

  12. J. Ahrens, P. Badzia̧g, A. Cabello, M. Bourennane, Nat. Phys. 8, 592 (2012). doi:10.1038/nphys2333

    Article  Google Scholar 

  13. M.M. Wolf, D. Pérez-García, Phys. Rev. Lett. 102, 190504 (2009). doi:10.1103/PhysRevLett.102.190504

    Article  ADS  MathSciNet  Google Scholar 

  14. J.S. Bell, Rev. Mod. Phys. 38, 447 (1966). doi:10.1103/RevModPhys.38.447

    Article  ADS  Google Scholar 

  15. S. Kochen, E.P. Specker, J. Math. Mech. 17, 59 (1967). doi:10.1512/iumj.1968.17.17004

    MathSciNet  Google Scholar 

  16. A.M. Gleason, J. Math. Mech. 6, 885 (1957)

    MathSciNet  Google Scholar 

  17. E.P. Specker, Dialectica 14, 239 (1960). doi:10.1111/dltc.1960.14.issue-2-3

    Article  MathSciNet  Google Scholar 

  18. Y.-C. Liang, R.W. Spekkens, H.M. Wiseman, Phys. Rep. 506, 1 (2011). doi:10.1016/j.physrep.2011.05.001

    Article  ADS  MathSciNet  Google Scholar 

  19. O. Gühne, C. Budroni, A. Cabello, M. Kleinmann, J.-Å. Larsson, Phys. Rev. A 89, 062107 (2014). doi:10.1103/PhysRevA.89.062107

    Article  ADS  Google Scholar 

  20. C. Budroni, C. Emary, Phys. Rev. Lett. 113, 050401 (2014). doi:10.1103/PhysRevLett.113.050401

    Article  ADS  Google Scholar 

  21. A.A. Klyachko, M.A. Can, S. Binicioğlu, A.S. Shumovsky, Phys. Rev. Lett. 101, 020403 (2008). doi:10.1103/PhysRevLett.101.020403

    Article  ADS  MathSciNet  Google Scholar 

  22. A. Peres, Quantum Theory: Concepts and Methods (Kluwer, Dordrecht, 1993)

    MATH  Google Scholar 

  23. M. Araújo, M.T. Quintino, C. Budroni, M. Terra Cunha, A. Cabello, Phys. Rev. A 88, 022118 (2013). doi:10.1103/PhysRevA.88.022118

  24. R. Łapkiewicz, P. Li, C. Schaeff, N.K. Langford, S. Ramelow, M. Wieśniak, A. Zeilinger, Nature (London) 474, 490 (2011). doi:10.1038/nature10119

    Article  Google Scholar 

  25. J. Ahrens, E. Amselem, A. Cabello, M. Bourennane, Sci. Rep. 3, 2170 (2013). doi:10.1038/srep02170

    Article  ADS  Google Scholar 

  26. O. Gühne, M. Kleinmann, A. Cabello, J.-Å Larsson, G. Kirchmair, F. Zähringer, R. Gerritsma, C.F. Roos. Phys. Rev. A 81, 022121 (2010). doi:10.1103/PhysRevA.81.022121

  27. T. Fritz, New J. Phys. 12, 083055 (2010). doi:10.1088/1367-2630/12/8/083055

    Google Scholar 

  28. A. Cabello, Phys. Rev. Lett. 101, 210401 (2008). doi:10.1103/PhysRevLett.101.210401

    Article  ADS  Google Scholar 

  29. A. Peres, Phys. Lett. A 151, 107 (1990). doi:10.1016/0375-9601(90)90172-K

    Article  ADS  MathSciNet  Google Scholar 

  30. N.D. Mermin, Phys. Rev. Lett. 65, 3373 (1990). doi:10.1103/PhysRevLett.65.3373

    Article  ADS  MathSciNet  Google Scholar 

  31. G. Kirchmair, F. Zähringer, R. Gerritsma, M. Kleinmann, O. Gühne, A. Cabello, R. Blatt, C.F. Roos, Nature (London) 460, 494 (2009). doi:10.1038/nature08172

    Article  ADS  Google Scholar 

  32. E. Amselem, M. Rådmark, M. Bourennane, A. Cabello, Phys. Rev. Lett. 103, 160405 (2009). doi:10.1103/PhysRevLett.103.160405

    Article  ADS  Google Scholar 

  33. O. Moussa, C.A. Ryan, D.G. Cory, R. Laflamme, Phys. Rev. Lett. 104, 160501 (2010). doi:10.1103/PhysRevLett.104.160501

    Article  ADS  MathSciNet  Google Scholar 

  34. C. Budroni, T. Moroder, M. Kleinmann, O. Gühne, Phys. Rev. Lett. 111, 020403 (2013). doi:10.1103/PhysRevLett.111.020403

    Article  ADS  Google Scholar 

  35. S. Yu, C.H. Oh, Phys. Rev. Lett. 108, 030402 (2012). doi:10.1103/PhysRevLett.108.030402

    Article  ADS  Google Scholar 

  36. M. Kleinmann, C. Budroni, J.-Å. Larsson, O. Gühne, A. Cabello, Phys. Rev. Lett. 109, 250402 (2012). doi:10.1103/PhysRevLett.109.250402

    Article  ADS  Google Scholar 

  37. A. Cabello, Phys. Rev. A 82, 032110 (2010). doi:10.1103/PhysRevA.82.032110

    Article  ADS  Google Scholar 

  38. A.J. Leggett, A. Garg, Phys. Rev. Lett. 54, 857 (1985). doi:10.1103/PhysRevLett.54.857

    Article  ADS  MathSciNet  Google Scholar 

  39. R.E. George, L.M. Robledo, O.J.E. Maroney, M.S. Blok, H. Bernien, M.L. Markham, D.J. Twitchen, J.J.L. Morton, G.A.D. Briggs, R. Hanson, Proc. Natl. Acad. Sci. USA 110, 3777 (2013). doi:10.1073/pnas.1208374110

    Article  ADS  Google Scholar 

  40. J. Kofler, Č. Brukner, Phys. Rev. Lett. 99, 180403 (2007). doi:10.1103/PhysRevLett.99.180403

    Article  ADS  Google Scholar 

  41. N. Lambert, R. Johansson, F. Nori, Phys. Rev. B 84, 245421 (2011). doi:10.1103/PhysRevB.84.245421

    Article  ADS  Google Scholar 

  42. M.M. Wilde, J.M. McCracken, A. Mizel, Proc. R. 5 Soc. A 466, 1347 (2010). doi:10.1098/rspa.2009.0575

    Google Scholar 

  43. B. Dakić, T. Paterek, Č. Brukner, New J. Phys. 16, 023028 (2014). doi:10.1088/1367-2630/16/2/023028

    Google Scholar 

  44. G. Lüders, Ann. Phys. (Leipzig) 8, 322 (1951)

    Google Scholar 

  45. J. von Neumann, Mathematische Grundlagen der Quantenmechanik (Springer, Berlin, 1932)

    MATH  Google Scholar 

  46. G. Lüders, English translation and discussion by K.A. Kirkpatrick. Ann. Phys. 15, 663 (2006). doi:10.1002/andp.200610207

    Google Scholar 

  47. B.C. Cirel’son, Lett. Math. Phys. 4, 93 (1980)

    Article  ADS  MathSciNet  Google Scholar 

  48. M. Markiewicz, P. Kurzynski, J. Thompson, S.-Y. Lee, A. Soeda, T. Paterek, D. Kaszlikowski, Phys. Rev. A 89, 042109 (2014). doi:10.1103/PhysRevA.89.042109

    Article  ADS  Google Scholar 

  49. S. Das, S. Aravinda, R. Srikanth, D. Home, Europhys. Lett. 104, 60006 (2013). doi:10.1209/0295-5075/104/60006

    Article  ADS  Google Scholar 

  50. Č. Brukner, S. Taylor, S. Cheung, V. Vedral (2004). arXiv:quant-ph/0402127

  51. S. Marcovitch and B. Reznik (2011). arXiv:1107.2186

  52. O. Oreshkov, F. Costa, Č. Brukner, Nat. Commun. 3, 1092 (2012). doi:10.1038/ncomms2076

    Article  ADS  Google Scholar 

  53. J. Fitzsimons, J. Jones, V. Vedral (2013). arXiv:1302.2731

  54. G.C. Hegerfeldt, R. Sala Mayato. Phys. Rev. A 85, 032116 (2012). doi:10.1103/PhysRevA.85.032116

  55. S.L. Braunstein C.M. Caves, Nucl. Phys. B Proc. Suppl. 6, 211 (1989). doi:10.1016/0920-5632(89)90441-6

    Google Scholar 

  56. S. Wehner, Phys. Rev. A 73, 022110 (2006). doi:10.1103/PhysRevA.73.022110

    Article  ADS  Google Scholar 

  57. M. Barbieri, Phys. Rev. A 80, 034102 (2009). doi:10.1103/PhysRevA.80.034102

    Article  ADS  Google Scholar 

  58. S. Popescu, D. Rohrlich, Found. Phys. 24, 379 (1994). doi:10.1007/BF02058098

    Google Scholar 

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  1. University of Siegen, Siegen, Germany

    Costantino Budroni

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Budroni, C. (2016). Dimension Witnesses. In: Temporal Quantum Correlations and Hidden Variable Models. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-319-24169-2_5

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