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Quantum Fisher information of an N-qubit maximal sliced state in decoherence channels and Ising-type interacting model

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  • Li, Yan
  • Ren, Zhihong

Abstract

Various quantum states have been suggested to realize high-precision measurement and quantum Fisher information (QFI) is one of the most important indicators to evaluate the performance. Here, we systematically investigate the QFI of an N-qubit maximal sliced (MS) state in different environments. In the ideal situation, we present the analytical QFI and it decays from N2 to (N−1)2 as the probability amplitude α changed from 0 to 1, which denotes the decreased metrological ability. In the amplitude damping channel, the variation trends of QFI with respect to the damping probability p are similar and it decreases to the number of qubits N at p=1, meaning the vanished entanglement superiority. However, it is different in the phase damping channel where with the increase of the number of qubits a turning point of QFI equal to N is found at p closing to 0.1. In the Ising-type interacting model, with the increasing interaction strength γ, the QFI with respect to α shows a crossover from decreasing to increasing. Particularly, at the critical point γ=1, the QFI of an N-qubit MS state is found analytically equal to N2 and regardless of α. This indicates a great potential in achieving the Heisenberg-limited metrology and may shed some new light on quantum information science.

Suggested Citation

  • Li, Yan & Ren, Zhihong, 2023. "Quantum Fisher information of an N-qubit maximal sliced state in decoherence channels and Ising-type interacting model," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).
    • Handle: RePEc:eee:chsofr:v:177:y:2023:i:c:s0960077923011918
    DOI: 10.1016/j.chaos.2023.114289
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    References listed on IDEAS

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    1. Abdel-Khalek, S. & Berrada, K. & Aldaghfag, Shatha A., 2021. "Quantum correlations and non-classical properties for two superconducting qubits interacting with a quantized field in the context of deformed Heisenberg algebra," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    2. Berrada, K., 2017. "Enhancing the precision of measurements in double quantum dot systems via transmission line resonator," Chaos, Solitons & Fractals, Elsevier, vol. 99(C), pages 2-6.
    3. Berrada, K. & Abdel-Khalek, S. & Khalil, E.M. & Alkaoud, A. & Eleuch, H., 2022. "Entanglement and Fisher information for a two-atom system interacting with deformed fields in correlated two-mode states," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    4. Li, Yan & Ren, Zhihong, 2022. "Nonlocal operation enhanced entanglement detection and classification," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 596(C).
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