On the Analytical Derivation of Quantum Fisher Information and Skew Information for two Qubit X States

Maroufi, B.; Laghmach, R.; Hadfi, H. El; Daoud, Mohammed

doi:10.1007/s10773-021-04907-9

Cited by 2 publications

(1 citation statement)

References 44 publications

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“…Doing so, also the QFI H(λ) can be decomposed in the sum of the QFI associated to the two matrices [55], as…”

Section: Fi and Qfimentioning

confidence: 99%

Characterization of partially accessible anisotropic spin chains in the presence of anti-symmetric exchange

Cavazzoni,

Adani,

Bordone

et al. 2024

New J. Phys.

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We address quantum characterization of anisotropic spin chains in the presence of anti-symmetric exchange, and investigate whether the Hamiltonian parameters of the chain may be estimated with precision approaching the ultimate limit imposed by quantum mechanics. At variance with previous approaches, we focus on the information that may be extracted by measuring only two neighboring spins rather than a global observable on the entire chain. We evaluate the Fisher information (FI) of a two-spin magnetization measure, and the corresponding quantum Fisher information (QFI), for all the relevant parameters, i.e. the spin coupling, the anisotropy, and the Dzyaloshinskii–Moriya (DM) parameter. Our results show that the reduced system made of two neighboring spins may be indeed exploited as a probe to characterize global properties of the entire system. In particular, we find that the ratio between the FI and the QFI is close to unit for a large range of the coupling values. The DM coupling is beneficial for coupling estimation, since it leads to the presence of additional bumps and peaks in the FI and QFI, which are not present in a model that neglects exchange interaction and may be exploited to increase the robustness of the overall estimation procedure. Finally, we address the multiparameter estimation problem, and show that the model is compatible but sloppy, i.e. both the Uhlmann curvature and the determinant of the QFI matrix vanish. Physically, this means that the state of the system actually depends only on a reduced numbers of combinations of parameters, and not on all of them separately.

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“…Doing so, also the QFI H(λ) can be decomposed in the sum of the QFI associated to the two matrices [55], as…”

Section: Fi and Qfimentioning

confidence: 99%

Characterization of partially accessible anisotropic spin chains in the presence of anti-symmetric exchange

Cavazzoni,

Adani,

Bordone

et al. 2024

New J. Phys.

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Critical metrology of minimally accessible anisotropic spin chains

Adani,

Cavazzoni,

Teklu

et al. 2024

Sci Rep

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We address quantum metrology in critical spin chains with anisotropy and Dzyaloshinskii–Moriya (DM) interaction, and show how local and quasi-local measurements may be exploited to characterize global properties of the systems. In particular, we evaluate the classical (magnetization) and quantum Fisher information of the relevant parameters for the density matrix of a single spin and that of a pair of spins ranging from nearest to sixth-nearest neighbors, to the limiting case of very distant spins. Our results allow us to elucidate the role of the different parameters and to individuate the optimal working regimes for the precise characterization of the system, also clarifying the effects of correlations on the estimation precision.

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On the Analytical Derivation of Quantum Fisher Information and Skew Information for two Qubit X States

Cited by 2 publications

References 44 publications

Characterization of partially accessible anisotropic spin chains in the presence of anti-symmetric exchange

Characterization of partially accessible anisotropic spin chains in the presence of anti-symmetric exchange

Critical metrology of minimally accessible anisotropic spin chains

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