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Foundations of Physics

, Volume 42, Issue 4, pp 531–543 | Cite as

Weak Measurement and Weak Information

  • Boaz TamirEmail author
  • Sergei Masis
Article

Abstract

Weak measurement devices resemble band pass filters: they strengthen average values in the state space or equivalently filter out some ‘frequencies’ from the conjugate Fourier transformed vector space. We thereby adjust a principle of classical communication theory for the use in quantum computation. We discuss some of the computational benefits and limitations of such an approach, including complexity analysis, some simple examples and a realistic not-so-weak approach.

Keywords

Quantum computation Quantum information Weak measurement Band pass filters Quantum filters 

Notes

Acknowledgements

We wish to thank the Interdisciplinary Center (IDC) in Herzliya for their hospitality at the academic year 2009–2010. We also wish to thank Daniel Rohlich for his explanations.

References

  1. 1.
    Starling, D.J., Dixon, P.B., Jordan, A.N., Howell, J.C.: Optimizing the signal to noise ratio of a beam deflection measurement with interferometric weak values. Phys. Rev. A 80 (2009) Google Scholar
  2. 2.
    Brillouin, L.: Science and Information Theory. Academic Press, New York (1956). (Reprint edition Dover, 2004). Chap. 15, pp. 202–228, Chap. 16, pp. 229–243 zbMATHGoogle Scholar
  3. 3.
    von Bayer, H.C.: Information: The New Language of Science. Harvard University Press, Cambridge (2005) Google Scholar
  4. 4.
    Landauer, R.: The physical nature of information. In: Leff, H.S., Rex, A.F. (eds.) Maxwell’s Demon 2, Institute of Physics Publishing, Bristol (2003) Google Scholar
  5. 5.
    Aharonov, Y., Rohrlich, D.: Quantum Paradoxes. Wiley-VCH, Weinheim (2005). Chap. 7, pp. 93–103, Chap. 16, pp. 225–248 zbMATHCrossRefGoogle Scholar
  6. 6.
    Vaidman, L.: Weak measurements, elements of reality. Found. Phys. 26(7) (1996) Google Scholar
  7. 7.
    Champeney, D.C.: Fourier Transforms and Their Physical Applications. Academic Press, San Diego (1973) zbMATHGoogle Scholar
  8. 8.
    Ballard, D.H., Brown, C.M.: Computer Vision. Prentice-Hall, New York (1982) Google Scholar
  9. 9.
    Schwartz, M., Shaw, L.: Signal Processing, Discrete Spectral Analysis, Detection and Estimation. McGraw-Hill, New York (1975) Google Scholar
  10. 10.
    Lomont, C.: Quantum convolution and quantum correlation algorithms are physically impossible. arxiv:quant-ph/0309070v2
  11. 11.
    Feller, W.: An Introduction to Probability Theory and Its Applications, vol. II. Wiley, New York (1972) Google Scholar
  12. 12.
    Peres, A.: Quantum Theory: Concepts and Methods. Kluwer Academic, Norwell (2002) CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Israel Institute for Advanced ResearchRehovotIsrael
  2. 2.Department of physicsTechnionHaifaIsrael

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