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Non-Classical Correlations in Information Processing

  • Anil ShajiEmail author
Chapter
Part of the Quantum Science and Technology book series (QST)

Abstract

In purely functional terms, a computation transforms a human readable bit string referred to as the input or question into another human readable bit string referred to as the output or answer. We are assuming here that irrespective of the nature of the input or output, information can always be expressed in the simplest possible language with only two elements in its alphabet; namely binary. In the process of getting from the input to the output, the sequence of steps - the algorithm - would employ additional resources like computational space (memory) computational time etc. Quantum information processing brings new resources into the mix; entanglement and quantum coherence being the the most prominent among them.

Notes

Acknowledgements

The technical content of this lecture note is based on work done - some of it published, some not - with several collaborators; particularly so with Animesh Datta, Carlton M Caves, Kavan Modi and Cesar Rodriguez-Rosario. The author’s role here was to primarily put some of the key ideas and results together into a coherent narrative.

References

  1. 1.
    D. Bruß, J. Math. Phys. 43, 4237 (2002)ADSMathSciNetCrossRefGoogle Scholar
  2. 2.
    R. Horodecki, P. Horodecki, M. Horodecki, K. Horodecki, Rev. Mod. Phys. 81, 865 (2009)Google Scholar
  3. 3.
    R. Jozsa, N. Linden, Proc. R. Soc. A Math. Phys. Eng. Sci. 459, 2011 (2003)Google Scholar
  4. 4.
    G. Vidal, Phys. Rev. Lett. 91, 147902 (2003)Google Scholar
  5. 5.
    M.A. Nielsen, I.L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, 2000)zbMATHGoogle Scholar
  6. 6.
    E. Knill, R. Laflamme, Phys. Rev. Lett. 81, 5672 (1998)ADSCrossRefGoogle Scholar
  7. 7.
    A. Datta, S.T. Flammia, C.M. Caves, Phys. Rev. A 72, 042316 (2005)ADSCrossRefGoogle Scholar
  8. 8.
    A. Datta, A. Shaji, C.M. Caves, Phys. Rev. Lett. 100, 050502 (2008)ADSCrossRefGoogle Scholar
  9. 9.
    H. Ollivier, W.H. Zurek, Phys. Rev. Lett. 88, 017901 (2001)ADSCrossRefGoogle Scholar
  10. 10.
    L. Henderson, V. Vedral, J. Phys. A Math. Gen. 34, 6899 (2001)ADSCrossRefGoogle Scholar
  11. 11.
    J. Emerson, Y.S. Weinstein, M. Saraceno, S. Lloyd, D.G. Cory, Science 302, 2098 (2003)ADSMathSciNetCrossRefGoogle Scholar
  12. 12.
    K. Modi, A. Brodutch, H. Cable, T. Paterek, V. Vedral, Rev. Mod. Phys. 84, 1655 (2012)ADSCrossRefGoogle Scholar
  13. 13.
    B. Dakic, V. Vedral, C. Brukner, Phys. Rev. Lett. 105, 190502 (2010)ADSCrossRefGoogle Scholar
  14. 14.
    B. Eastin, Simulating Concordant Computations (2010). arXiv:quant-ph/1006.4402
  15. 15.
    H. Cable, D.E. Browne, New J. Phys. 17, 113049 (2015)ADSCrossRefGoogle Scholar
  16. 16.
    S. Luo, Phys. Rev. A 77, 022301 (2008)ADSCrossRefGoogle Scholar
  17. 17.
    S. Wu, U.V. Poulsen, K. Mølmer, Phys. Rev. A 80, 032319 (2009)ADSCrossRefGoogle Scholar
  18. 18.
    W.H. Zurek, Phys. Rev. A 67, 012320 (2003)ADSCrossRefGoogle Scholar
  19. 19.
    M.D. Lang, C.M. Caves, A. Shaji, Int. J. Quanum Inf. 09, 1553 (2011)CrossRefGoogle Scholar
  20. 20.
    T.S. Cubitt, F. Verstraete, W. Dür, J.I. Cirac, Phys. Rev. Lett. 91, 037902 (2003)ADSCrossRefGoogle Scholar
  21. 21.
    T.K. Chuan, J. Maillard, K. Modi, T. Paterek, M. Paternostro, M. Piani, arXiv:1203.1268 (2012)
  22. 22.
    A. Streltsov, H. Kampermann, D. Bruß, arXiv:1203.1264 (2012)
  23. 23.
    A. Datta, Studies on the Role of Entanglement in Mixed-state Quantum Computation, Ph.D. thesis, University of New Mexico, 2008Google Scholar
  24. 24.
    H.P. Breuer, F. Petruccione, The Theory of Open Quantum Systems (Oxford University Press, New York, 2002)zbMATHGoogle Scholar
  25. 25.
    E.B. Davies, Quantum Theory of Open Systems (Academic Press, New York, 1976)zbMATHGoogle Scholar
  26. 26.
    B. Schumacher, Phys. Rev. A 54, 2614 (1996)ADSCrossRefGoogle Scholar
  27. 27.
    K. Kraus, States, Effects and Operations: Fundamental Notions of Quantum Theory, ed. by A. Bohm, J. D. Dollard, W.H. Wooters. Lecture Notes in Physics, vol. 190 (Springer, New York, 1983)Google Scholar
  28. 28.
    W.F. Stinespring, Proc. Am. Math. Soc. 6, 211 (1955)MathSciNetGoogle Scholar
  29. 29.
    P. Pechukas, Phys. Rev. Lett. 73, 1060 (1994)ADSMathSciNetCrossRefGoogle Scholar
  30. 30.
    P. Pechukas, Phys. Rev. Lett. 75, 3021 (1995)ADSCrossRefGoogle Scholar
  31. 31.
    T.F. Jordan, A. Shaji, E.C.G. Sudarshan, Phys. Rev. A 70, 52110 (2004)ADSMathSciNetCrossRefGoogle Scholar
  32. 32.
    A. Shaji, E.C.G. Sudarshan, Phys. Lett. A. 341, 48 (2005)ADSMathSciNetCrossRefGoogle Scholar
  33. 33.
    F. Buscemi, Phys. Rev. Lett. 113, 140502 (2014)ADSCrossRefGoogle Scholar
  34. 34.
    C.A. Rodriguez, K. Modi, A. meng Kuah, A. Shaji, E.C.G. Sudarshan, J. Phys. A Math. Theor. 41, 205301 (2008)Google Scholar
  35. 35.
    A. Datta, A. Shaji, Int. J. Quantum Inf. 09, 1787 (2011)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.School of PhysicsIndian Institute of Science Education and Research ThiruvananthapuramVithura, ThiruvananthapuramIndia

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