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Tracing of an Entanglement Level in Short Qubit and Qutrit Spin Chains

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Computer Networks (CN 2015)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 522))

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Abstract

The phenomenon of quantum entanglement is an important component of many protocols in the field of quantum computing. In this paper a level of entanglement in short qudit chains is evaluated. The evaluation is carried out with use of the CCNR criterion and the concurrence measure. There are also some explicit formulae describing the values of CCNR criterion and concurrence for exemplary short spin chains. Mentioned formulae may be used as an invariant for a protocol which describes a transfer of information in XY-like spin chains.

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References

  1. Horodecki, R., Horodecki, P., Horodecki, M., Horodecki, K.: Quantum entanglement. Rev. Mod. Phys. 81, 865–942 (2009)

    MATH  MathSciNet  Google Scholar 

  2. Hirvensalo, M.: Quantum Computing. Springer, Berlin (2001)

    Book  MATH  Google Scholar 

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

    MATH  Google Scholar 

  4. Klamka, J., Węgrzyn, S., Znamirowski, L., Winiarczyk, R., Nowak, S.: Nano and quantum systems of informatics. Bull. Pol. Acad. Sci.: Tech. Sci. 52(1), 1–10 (2004)

    MATH  Google Scholar 

  5. Jafarizadeh, M.A., Sufiani, R., Taghavi, S.F., Barati, E.: Optimal transfer of a d-level quantum state over pseudo-distance-regular networks. J. Phys. A Math. Theor. 41, 475302 (2008)

    MathSciNet  Google Scholar 

  6. Paz-Silva, G.A., Rebić, S., Twamley, J., Duty, T.: Perfect mirror transport protocol with higher dimensional quantum chains. Phys. Rev. Lett. 102, 020503 (2009)

    Google Scholar 

  7. Bayat, A.: Arbitrary perfect state transfer in \(d\)-level spin chains. Phys. Rev. A 89(6), 062302 (2014)

    Google Scholar 

  8. Bose, S.: Quantum communication through an unmodulated spin chain. Phys. Rev. Lett. 91, 207901 (2003)

    Google Scholar 

  9. Bose, S.: Quantum communication through spin chain dynamics: an introductory overview. Contemp. Phys. 48, 13–30 (2007)

    Google Scholar 

  10. Vinet, L., Zhedanov, A.: How to construct spin chains with perfect state transfer. Phys. Rev. A 85, 012323 (2012)

    Google Scholar 

  11. Kay, A.: A review of perfect state transfer and its application as a constructive tool. Int. J. Quantum Inf. 8(4), 641–676 (2010)

    MATH  MathSciNet  Google Scholar 

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

    MATH  MathSciNet  Google Scholar 

  13. Klamka, J., Gawron, P., Miszczak, J., Winiarczyk, R.: Structural programming in quantum octave. Bull. Pol. Acad. Sci. Tech. Sci. 58(1), 77–88 (2010)

    Google Scholar 

  14. Chen, K., Albeverio, S., Fei, S.M.: Concurrence of arbitrary dimensional bipartite quantum states. Phys. Rev. Lett. 95, 040504 (2005)

    MathSciNet  Google Scholar 

  15. Rudolph, O.: Some properties of the computable cross-norm criterion for separability. Phys. Rev. A 67, 032312 (2003)

    MathSciNet  Google Scholar 

  16. Zhang, C.J., Zhang, Y.S., Zhang, S., Guo, G.C.: Entanglement detection beyond the computable cross-norm or realignment criterion. Phys. Rev. A 77, 060301(R) (2008)

    Google Scholar 

  17. Almutairi, K., Tanaś, R., Ficek, Z.: Generating two-photon entangled states in a driven two-atom system. Phys. Rev. A 84, 013831 (2011)

    Google Scholar 

  18. Wang, Z.H., Wang, B.S., Su, Z.B.: Entanglement evolution of a spin-chain bath coupled to a quantum spin. Phys. Rev. B 79, 104428 (2009)

    Google Scholar 

  19. Gawron, P., Klamka, J., Winiarczyk, R.: Noise effects in the quantum search algorithm from the viewpoint of computational complexity. Int. J. Appl. Math. Comput. Sci. 22(2), 493–499 (2012)

    MATH  MathSciNet  Google Scholar 

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Acknowledgments

We would like to thank for useful discussions with the Q-INFO group at the Institute of Control and Computation Engineering (ISSI) of the University of Zielona Góra, Poland. We would like also to thank to anonymous referees for useful comments on the preliminary version of this paper. The numerical results were done using the hardware and software available at the “GPU \(\mu \)-Lab” located at the Institute of Control and Computation Engineering of the University of Zielona Góra, Poland.

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Authors and Affiliations

  1. Institute of Control and Computation Engineering, University of Zielona Góra, Licealna 9, 65-417, Zielona Góra, Poland

    Marek Sawerwain

  2. Institute of Information Systems, Faculty of Cybernetics, Military University of Technology, Kaliskiego 2, 00-908, Warsaw, Poland

    Joanna Wiśniewska

Authors
  1. Marek Sawerwain
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  2. Joanna Wiśniewska
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Corresponding author

Correspondence to Marek Sawerwain .

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Editors and Affiliations

  1. Silesian University of Technology, Gliwice, Poland

    Piotr Gaj

  2. Silesian University of Technology, Gliwice, Poland

    Andrzej Kwiecień

  3. Silesian University of Technology, Gliwice, Poland

    Piotr Stera

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Sawerwain, M., Wiśniewska, J. (2015). Tracing of an Entanglement Level in Short Qubit and Qutrit Spin Chains. In: Gaj, P., Kwiecień, A., Stera, P. (eds) Computer Networks. CN 2015. Communications in Computer and Information Science, vol 522. Springer, Cham. https://doi.org/10.1007/978-3-319-19419-6_26

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  • DOI: https://doi.org/10.1007/978-3-319-19419-6_26

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-19418-9

  • Online ISBN: 978-3-319-19419-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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