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Generalized discord, entanglement, Einstein–Podolsky–Rosen steering, and Bell nonlocality in two-qubit systems under (non-)Markovian channels: Hierarchy of quantum resources and chronology of deaths and births

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  • Costa, A.C.S.
  • Beims, M.W.
  • Angelo, R.M.

Abstract

Generalized quantum discord (Dq), Einstein–Podolsky–Rosen steering (S), entanglement (E), and Bell nonlocality (N), are logically distinct quantifiers of quantum correlations. All these measures capture nonclassical aspects of quantum states and play some role as resources in quantum information processing. In this work, we look for the hierarchy satisfied by these quantum correlation witnesses for a class of two-qubit states. We show that N⊳S⊳E⊳Dq, meaning that nonlocality implies steering, which in turn implies entanglement, which then implies q-discord. For the quantum states under concern, we show that the invariance of this hierarchy under noisy quantum channels directly implies a death chronology. Additionally, we have found that sudden death of all quantum resources except discord is absent only for a subset of states of measure zero. At last, we provide an illustration of another consequence of the aforementioned hierarchy, namely, the existence of a sudden birth chronology under non-Markovian channels.

Suggested Citation

  • Costa, A.C.S. & Beims, M.W. & Angelo, R.M., 2016. "Generalized discord, entanglement, Einstein–Podolsky–Rosen steering, and Bell nonlocality in two-qubit systems under (non-)Markovian channels: Hierarchy of quantum resources and chronology of deaths a," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 461(C), pages 469-479.
    • Handle: RePEc:eee:phsmap:v:461:y:2016:i:c:p:469-479
    DOI: 10.1016/j.physa.2016.05.068
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    References listed on IDEAS

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    1. Charles H. Bennett & David P. DiVincenzo, 2000. "Quantum information and computation," Nature, Nature, vol. 404(6775), pages 247-255, March.
    2. L. Steffen & Y. Salathe & M. Oppliger & P. Kurpiers & M. Baur & C. Lang & C. Eichler & G. Puebla-Hellmann & A. Fedorov & A. Wallraff, 2013. "Deterministic quantum teleportation with feed-forward in a solid state system," Nature, Nature, vol. 500(7462), pages 319-322, August.
    3. Zeeya Merali, 2011. "Quantum computing: The power of discord," Nature, Nature, vol. 474(7349), pages 24-26, June.
    4. Shuntaro Takeda & Takahiro Mizuta & Maria Fuwa & Peter van Loock & Akira Furusawa, 2013. "Deterministic quantum teleportation of photonic quantum bits by a hybrid technique," Nature, Nature, vol. 500(7462), pages 315-318, August.
    5. Devin H. Smith & Geoff Gillett & Marcelo P. de Almeida & Cyril Branciard & Alessandro Fedrizzi & Till J. Weinhold & Adriana Lita & Brice Calkins & Thomas Gerrits & Howard M. Wiseman & Sae Woo Nam & An, 2012. "Conclusive quantum steering with superconducting transition-edge sensors," Nature Communications, Nature, vol. 3(1), pages 1-6, January.
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    Cited by:

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