Frontiers of Physics

, Volume 9, Issue 5, pp 629–633 | Cite as

Temporal inequalities for sequential multi-time actions in quantum information processing

  • Marek Żukowski
Research Article


A new kind of temporal inequalities are discussed, which apply to algorithmic processes, involving a finite memory processing unit. They are an alternative to the Leggett-Grag ones, as well as to the modified ones by Brukner et al. If one considers comparison of quantum and classical processes involving systems of finite memory (of the same capacity in both cases), the inequalities give a clear message why we can expect quantum speed-up. In a classical process one always has clearly defined values of possible measurements, or in terms of the information processing language, if we have a sequential computations of some function depending on data arriving at each step on an algorithm, the function always has a clearly defined value. In the quantum case only the final value, after the end of the algorithm, is defined. All intermediate values, in agreement with Bohr’s complementarity, cannot be ascribed a definite value.


temporal inequalities quantum information 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References and notes

  1. 1.
    Č. Brukner, S. Taylor, S. Cheung, and V. Vedral, Quantum entanglement in time, arXiv: quant-ph/0402127, 2004Google Scholar
  2. 2.
    A. J. Leggett and A. Garg, Quantum Mechanics versus macroscopic realism: is the flux there when nobody looks? Phys. Rev. Lett., 1985, 54(9): 857MathSciNetCrossRefADSGoogle Scholar
  3. 3.
    A. J. Leggett, Testing the limits of quantum mechanics: Motivation, state of play, prospects, J. Phys.: Condens. Matter, 2002, 14(15): R415ADSGoogle Scholar
  4. 4.
    A. J. Leggett, Realism and the physical world, Rep. Prog. Phys., 2008, 71(2): 022001MathSciNetCrossRefADSGoogle Scholar
  5. 5.
    M. Żukowski, Quantum Speedup and Temporal Inequalities for Sequential Actions, in: Computable Universe, edited by H. Zenil, World Scientific/Imperial College, Singapore, London, 2012Google Scholar
  6. 7.
    M. Kleinmann, O. Gühne, J. R. Portillo, J. A. Larsson, and A. Cabello, Memory cost of quantum contextuality, New J. Phys., 2011, 13(11): 113011CrossRefADSGoogle Scholar
  7. 8.
    P. Trojek, Ch. Schmid, M. Bourennane, Č. Brukner, M. Żukowski, and H. Weinfurter,, Experimental quantum communication complexity, Phys. Rev. A, 2005, 72(5): 050305(R)CrossRefADSGoogle Scholar
  8. 9.
    Č. Brukner, M. Żukowski, J.W. Pan, and A. Zeilinger,, Bell’s inequality and quantum communication complexity, Phys. Rev. Lett., 2004, 92(12): 127901MathSciNetCrossRefADSGoogle Scholar
  9. 10.
    J.W. Pan, Z. B. Chen, C. Y. Lu, H. Weinfurter, A. Zeilinger, and M. Żukowski,, Multiphoton entanglement and interferometry, Rev. Mod. Phys., 2012, 84(2): 777CrossRefADSGoogle Scholar
  10. 11.
    A. Shafiee and M. Golshani, Single-particle Bell-type inequality, Annales Fond. Broglie, 2003, 28: 105MathSciNetGoogle Scholar
  11. 12.
    F. Morikoshi, Informationtheoretic temporal Bell inequality and quantum computation, Phys. Rev. A, 2006, 73(5): 052308CrossRefADSGoogle Scholar
  12. 13.
    J. Kofler, Quantum violation of macroscopic realism and the transition to classical physics, Ph. D. Thesis, arXiv: 0812.0238, 2008Google Scholar
  13. 14.
    J. Kofler and Č. Brukner, The conditions for quantum violation of macroscopic realism, Phys. Rev. Lett., 2008, 101(9): 090403CrossRefADSGoogle Scholar
  14. 15.
    J. Kofler, N. Buric, and Č. Brukner, Macroscopic realism and spatiotemporal continuity, arXiv: 0906.4465, 2009Google Scholar

Copyright information

© Higher Education Press and Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Institute for Theoretical Physics and AstrophysicsUniwersytet GdańskiGdańskPoland
  2. 2.Hefei National Laboratory of Physical Sciences at the MicroscaleUniversity of Science and Technology of ChinaHefeiChina

Personalised recommendations