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International Conference on Computer Networks

CN 2009: Computer Networks pp 11–18Cite as

Sorting of Quantum States with Respect to Amount of Entanglement Included

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Part of the book series: Communications in Computer and Information Science ((CCIS,volume 39))

Abstract

The canonical Schmidt decomposition of quantum states is discussed and its implementation to the Quantum Computation Simulator is outlined. In particular, the semiorder relation in the space of quantum states induced by the lexicographic semiorder of the space of the Schmidt coefficients is discussed. The appropriate sorting algorithms on the corresponding POSETs (partial ordered sets) consisting from quantum states are formulated and theirs computer implementations are being tested.

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References

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

    MATH  Google Scholar 

  2. Garey, M.R., Johnson, D.S.: Computers and Intractability: A guide to the Theory of NP-Completeness. W.H.Freeman and Co., San Francisco (1979)

    MATH  Google Scholar 

  3. Papadimitrio, C.H.: Computational Complexity. Addison-Wesley, Reading (1994)

    Google Scholar 

  4. Nielsen, M.A.: Conditions for a class of entanglement transformations. Phys. Rev. Lett. 83, 436 (1999)

    Article  Google Scholar 

  5. Gurvits, L.: Classical deterministic complexity of Edmonds – problem and Quantum Entanglement. In: Proc. of the 35th Annual ACM Symposium on Theory of Computing, San Diego, USA, June 9-11 (2003), also available at quant-ph/0303055

    Google Scholar 

  6. Daskalakis, C., Karp, R.M., Mossel, E., Riesenfeld, S., Verbin, E.: Sorting and Selectio In Posets, http://arxiv.org/abs/0707.1532

  7. Faigle, U., Turan, G.: Sorting and Recognition Problems for ordered Sets. SIAM J. Comput. 17(1), 100–113 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  8. Gielerak, R., Sawerwain, M.: Sorting of amount of Entanglement in Quantum States functions implemented for Quantum Computing Simulator. Submitted to KNWS 2009 conference, www.knws.uz.zgora.pl

  9. Terhall, B.M., Horodecki, P.: arXiv:quant-ph/9911117v4

    Google Scholar 

  10. Chen, K., Wu, L.A.: Quant. Inf. Comp. 3, 193 (2003)

    Google Scholar 

  11. Rudolph, O.: Phys. Rev. A 67, 032312 (2003)

    Google Scholar 

  12. Gielerak, R., Sawerwain, M. (in preparations)

    Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Institute of Control & Computation Engineering, University of Zielona Góra, ul. Podgórna 50, Zielona Góra, 65-246, Poland

    Roman Gielerak & Marek Sawerwain

Authors
  1. Roman Gielerak
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  2. Marek Sawerwain
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Editor information

Editors and Affiliations

  1. Institute of Informatics, Silesian University of Technology, Gliwice, Poland

    Andrzej Kwiecień , Piotr Gaj  & Piotr Stera ,  & 

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© 2009 Springer-Verlag Berlin Heidelberg

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Gielerak, R., Sawerwain, M. (2009). Sorting of Quantum States with Respect to Amount of Entanglement Included. In: Kwiecień, A., Gaj, P., Stera, P. (eds) Computer Networks. CN 2009. Communications in Computer and Information Science, vol 39. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02671-3_2

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  • DOI: https://doi.org/10.1007/978-3-642-02671-3_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-02670-6

  • Online ISBN: 978-3-642-02671-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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