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Information geometry of quantum entangled Gaussian wave-packets

Author

Listed:
  • Kim, D.-H.
  • Ali, S.A.
  • Cafaro, C.
  • Mancini, S.

Abstract

We apply information geometric (IG) techniques to study s-wave, scattering-induced quantum entanglement. Application of IG methods enables use of statistical manifolds associated with correlated and non-correlated Gaussian probability distribution functions to model the quantum entanglement of two spinless, structureless, non-relativistic particles, the latter represented by minimum uncertainty Gaussian wave-packets. Our analysis leads to the following relevant findings: first, we are able to express the entanglement strength, quantified by the subsystem purity, in terms of scattering potential and incident particle energies, which in turn, are related to the micro-correlation coefficient r, a quantity that parameterizes the correlated microscopic degrees of freedom of the system; second, we show that the entanglement duration can be controlled by the initial momentum po, momentum spread σo and r. Finally, we uncover a quantitative relation between quantum entanglement and information geometric complexity.

Suggested Citation

  • Kim, D.-H. & Ali, S.A. & Cafaro, C. & Mancini, S., 2012. "Information geometry of quantum entangled Gaussian wave-packets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(19), pages 4517-4556.
    • Handle: RePEc:eee:phsmap:v:391:y:2012:i:19:p:4517-4556
    DOI: 10.1016/j.physa.2012.04.023
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    Cited by:

    1. Cafaro, Carlo, 2017. "Geometric algebra and information geometry for quantum computational software," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 470(C), pages 154-196.
    2. Gomez, Ignacio S. & Portesi, Mariela & Borges, Ernesto P., 2020. "Universality classes for the Fisher metric derived from relative group entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 547(C).

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