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A simple analytical expression of quantum Fisher and Skew information and their dynamics under decoherence channels

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  • Abouelkhir, N.
  • EL Hadfi, H.
  • Slaoui, A.
  • Ahl Laamara, R.

Abstract

In statistical estimation theory, it has been shown previously that the Wigner–Yanase skew information is bounded by the quantum Fisher information associated with the phase parameter. Besides, the quantum Cramér–Rao inequality is expressed in terms of skew information. Since these two fundamental quantities are based on the concept of quantum uncertainty, we derive here their analytical formulas for arbitrary two qubit X-states using the same analytical procedures. A comparison of these two informational quantifiers for two quasi-Werner states composed of two bipartite superposed coherent states is examined. Moreover, we investigated the decoherence effects on such quantities generated by the phase damping, depolarization and amplitude damping channels. We showed that decoherence strongly influences the quantum criteria during the evolution and these quantities exhibit similar dynamic behaviors. This current work is characterized by the fact that these two concepts play the same role and capture similar properties in quantum estimation protocols.

Suggested Citation

  • Abouelkhir, N. & EL Hadfi, H. & Slaoui, A. & Ahl Laamara, R., 2023. "A simple analytical expression of quantum Fisher and Skew information and their dynamics under decoherence channels," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 612(C).
    • Handle: RePEc:eee:phsmap:v:612:y:2023:i:c:s0378437123000341
    DOI: 10.1016/j.physa.2023.128479
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    References listed on IDEAS

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    1. Max F. Riedel & Pascal Böhi & Yun Li & Theodor W. Hänsch & Alice Sinatra & Philipp Treutlein, 2010. "Atom-chip-based generation of entanglement for quantum metrology," Nature, Nature, vol. 464(7292), pages 1170-1173, April.
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    3. Hosung Seo & Abram L. Falk & Paul V. Klimov & Kevin C. Miao & Giulia Galli & David D. Awschalom, 2016. "Quantum decoherence dynamics of divacancy spins in silicon carbide," Nature Communications, Nature, vol. 7(1), pages 1-9, December.
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