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Quantum state transfer in spin chains with q-deformed interaction terms

Elchin Jafarov (UGent) and Joris Van der Jeugt (UGent)
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Abstract
We study the time evolution of a single spin excitation state in certain linear spin chains, as a model for quantum communication. Some years ago it was discovered that when the spin chain data (the nearest-neighbour interaction strengths and the magnetic field strengths) are related to the Jacobi matrix entries of Krawtchouk polynomials or dual Hahn polynomials the so-called perfect state transfer takes place. The extension of these ideas to other types of discrete orthogonal polynomials did not lead to new models with perfect state transfer, but did allow more insight in the general computation of the correlation function. In this paper, we extend the study to discrete orthogonal polynomials of q-hypergeometric type. A remarkable result is a new analytic model where perfect state transfer is achieved: this is when the spin chain data are related to the Jacobi matrix of q-Krawtchouk polynomials. The other cases studied here (affine q-Krawtchouk polynomials, quantum q-Krawtchouk polynomials, dual q-Krawtchouk polynomials, q-Hahn polynomials, dual q-Hahn polynomials and q-Racah polynomials) do not give rise to models with perfect state transfer. However, the computation of the correlation function itself is quite interesting, leading to advanced q-series manipulations.
Keywords
Orthogonal polynomials, linear spin chains, quantum communication, perfect state transfer, Jacobi matrix

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MLA
Jafarov, Elchin, and Joris Van der Jeugt. “Quantum State Transfer in Spin Chains with Q-Deformed Interaction Terms.” JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, vol. 43, no. 40, 2010, doi:10.1088/1751-8113/43/40/405301.
APA
Jafarov, E., & Van der Jeugt, J. (2010). Quantum state transfer in spin chains with q-deformed interaction terms. JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 43(40). https://doi.org/10.1088/1751-8113/43/40/405301
Chicago author-date
Jafarov, Elchin, and Joris Van der Jeugt. 2010. “Quantum State Transfer in Spin Chains with Q-Deformed Interaction Terms.” JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL 43 (40). https://doi.org/10.1088/1751-8113/43/40/405301.
Chicago author-date (all authors)
Jafarov, Elchin, and Joris Van der Jeugt. 2010. “Quantum State Transfer in Spin Chains with Q-Deformed Interaction Terms.” JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL 43 (40). doi:10.1088/1751-8113/43/40/405301.
Vancouver
1.
Jafarov E, Van der Jeugt J. Quantum state transfer in spin chains with q-deformed interaction terms. JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL. 2010;43(40).
IEEE
[1]
E. Jafarov and J. Van der Jeugt, “Quantum state transfer in spin chains with q-deformed interaction terms,” JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, vol. 43, no. 40, 2010.
@article{1047994,
  abstract     = {{We study the time evolution of a single spin excitation state in certain linear spin chains, as a model for quantum communication. Some years ago it was discovered that when the spin chain data (the nearest-neighbour interaction strengths and the magnetic field strengths) are related to the Jacobi matrix entries of Krawtchouk polynomials or dual Hahn polynomials the so-called perfect state transfer takes place. The extension of these ideas to other types of discrete orthogonal polynomials did not lead to new models with perfect state transfer, but did allow more insight in the general computation of the correlation function. In this paper, we extend the study to discrete orthogonal polynomials of q-hypergeometric type. A remarkable result is a new analytic model where perfect state transfer is achieved: this is when the spin chain data are related to the Jacobi matrix of q-Krawtchouk polynomials. The other cases studied here (affine q-Krawtchouk polynomials, quantum q-Krawtchouk polynomials, dual q-Krawtchouk polynomials, q-Hahn polynomials, dual q-Hahn polynomials and q-Racah polynomials) do not give rise to models with perfect state transfer. However, the computation of the correlation function itself is quite interesting, leading to advanced q-series manipulations.}},
  articleno    = {{405301}},
  author       = {{Jafarov, Elchin and Van der Jeugt, Joris}},
  issn         = {{1751-8113}},
  journal      = {{JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL}},
  keywords     = {{Orthogonal polynomials,linear spin chains,quantum communication,perfect state transfer,Jacobi matrix}},
  language     = {{eng}},
  number       = {{40}},
  pages        = {{18}},
  title        = {{Quantum state transfer in spin chains with q-deformed interaction terms}},
  url          = {{http://dx.doi.org/10.1088/1751-8113/43/40/405301}},
  volume       = {{43}},
  year         = {{2010}},
}

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