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Chaos Solitons & Fractals

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

Yan Li, Zhihong Ren

Published Nov 18, 2023• 2 citations
Publisher
DOI
10.1016/j.chaos.2023.114289

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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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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 parameter 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 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. PACS: 03.67.-a, 03.65.Ud

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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 parameter 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 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. PACS: 03.67.-a, 03.65.Ud
Abstract From the perspective of nonlocal operation, we investigate the Quantum Fisher information of N-qubit W and GHZ superposition state. Taking advantage of the general Ising model and Lipkin-Meshkov-Glick model, we analytically present the QFI of N-qubit superposition state. Evidently the traditional fixed QFI is changed and largely increased. As an paradigm, we numerically study the QFI of 3-qubit superposition state with respect to ratio α and interaction strength ε, and find the trends of QFI in both models are similar. There always exists a turning point for QFI and the α is around 0.7. Interestingly, for the interaction strength ε = 1 in Ising model, the well-known Heisenberg limit is almost achieved for all α. Moreover, under the same interaction strength, we compare the QFI of N-qubit superposition state in both models. With the increasing qubits involved, the α for maximal QFI in Ising model is changed from close to 1 to the middle region, while it is different in Lipkin-Meshkov-Glick model and the α is close to 1.
We investigate the entanglement robustness of an N-qubit W superposition state against particle loss with quantum Fisher information. In the noninteracting environment, the quantum Fisher information of reduced W superposition state is found same as it from W superposition state when the number of qubits is larger than 5, which shows very strong entanglement robustness compared to Twin-Fock state and Greenberger-Horne-Zeilinger state. Meanwhile, the re-particle-loss effect is also studied and it presents a rapid decay of quantum Fisher information with the increase of the number of losing qubits, indicating the weak entanglement robustness. In the Ising-type interacting environment, the results show that reduced W superposition state performs better than it in noninteracting environment. With the increasing qubits (N>5) the reduced W superposition state behaves much more robust than original W state. To simulate a real noisy environment, the effects of different decoherence channels are also considered.