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Quantum metrology with superposition of GHZ state and Twin-Fock state

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  • Li, Yan
  • Ren, Zhihong

Abstract

We study the metrological performance of the superposition of Greenberger–Horne–Zeilinger state and Twin Fock state (SGT) in quantum phase estimation. The analytical quantum Fisher information (QFI) of an N-qubit SGT state in noninteracting environment has been derived and with the increasing ratio β in SGT state it emerges a turning point at critical βt=1−1N⋅23, where the smallest QFI FQ=(N2+2N)/3 is achieved. Interestingly, we find the 4-qubit SGT state performs better than TF state in all ratio region and further achieves the Heisenberg limit at β=3/2. Working in the Mach–Zehnder interferometry, we have provided the optimal metrology schemes saturated by quantum CRLB for all kinds of SGT states and found the same βt also exists in the selection of phase generator and measured parity operator. Moreover, we have considered the decoherence effects and with the increasing decay the QFI in amplitude damping and phase damping channel decrease to the number of qubits involved, while it decreases to zero in depolarizing channel. Specially, the 4-qubit SGT state of β=3/2 is found to perform better than GHZ state in phase damping channel. Our work enriches the metrological useful quantum resources.

Suggested Citation

  • Li, Yan & Ren, Zhihong, 2024. "Quantum metrology with superposition of GHZ state and Twin-Fock state," Chaos, Solitons & Fractals, Elsevier, vol. 186(C).
    • Handle: RePEc:eee:chsofr:v:186:y:2024:i:c:s0960077924008518
    DOI: 10.1016/j.chaos.2024.115299
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    References listed on IDEAS

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    1. Li, Yan & Ren, Zhihong, 2022. "Nonlocal operation enhanced entanglement detection and classification," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 596(C).
    2. Christian D. Marciniak & Thomas Feldker & Ivan Pogorelov & Raphael Kaubruegger & Denis V. Vasilyev & Rick Bijnen & Philipp Schindler & Peter Zoller & Rainer Blatt & Thomas Monz, 2022. "Optimal metrology with programmable quantum sensors," Nature, Nature, vol. 603(7902), pages 604-609, March.
    3. 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).
    4. 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.
    5. Roman Schnabel & Nergis Mavalvala & David E. McClelland & Ping K. Lam, 2010. "Quantum metrology for gravitational wave astronomy," Nature Communications, Nature, vol. 1(1), pages 1-10, December.
    Full references (including those not matched with items on IDEAS)

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