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Description
This study is concerned with the investigation of the continuity of Quantum Fisher Information (QFI) between two states, one experimentally generated , σ=(σ,∂_x σ), and one theoretically derived, ρ=(ρ,∂_x ρ), in different systems such as qubits, exponential density matrices and noise-free quantum dynamics [1, 2, 3, 4].
In quantum parameter estimation, the QFI exhibits universal continuity, where neighboring states with similar derivatives have nearly equal QFIs [1, 5, 6]. This property, independent of the dynamics or the form of parameter detection, extends the classical Fisher information concept to density matrices [7, 8, 9].
The investigation aims at determining the minimum error and defining the lower bound for ΔF^Q=|F^Q (ρ)-F^Q (σ)|. Calculations of the relative error are discussed, ranging from Δ_min to Δ_max indicating that if the ΔF^Q values are close to each other, the relative error has been adequately accounted for in the experimental calculations; otherwise, recalibration may be required [1, 10].
References
[1] Ali Rezakhani, Majid Hassani,and Sahar Alipour, "Continuity of the quantum Fisher information," PHYSICAL REVIEW A 100, 032317, 2019.
[2] Aashish A. Clerk, «Quantum Noise and quantum measurement,», Oxford University Press, 13 December 2021.
[3] Umut Parlak and Géza Tóth, «Quantum Noise in Quantum Thermodynamics,», Physical Review Research, 2021.
[4] S. M. Roy and Samuel L. Braunstein, «Exponentially Enhanced Quantum Metrology,», Phys. Rev. Lett. 100,220501, 2008.
[5] Seth Lloyd,Giacomo De Palma,Can Gokler,Bobak Kiani,Zi-Wen Liu,Milad Marvian,Felix Tennie,Tim Palmer, "Quantum algorithm for nonlinear differential equations," arxiv.org/abs/2011.06571v2.
[6] M. G. A. Paris, «QUANTUM ESTIMATION for QUANTUM TECHNOLOGY,», Int. J. Quantum. Inf. 07, 125 , 2009..
[7] &. I. ,. Michael A Nielsen, «Quantum computation and quantum information,», Cambridge University Press, 2010..
[8] J. C. X.-X. J. X. W. Jing Liu, «Quantum Fisher information and symmetric logarithmic derivative via anti-commutators,», J. Phys. A: Math.Theor. 49, 275302, 2016. .
[9] D. A. Lidar, «Lecture Notes on the Theory of Open Quantum Systems,», arxiv. 1902.00967v2, 21 Feb 2020..
[10] Vittorio Giovannetti, Seth Lloyd, and Lorenzo Maccone, "Quantum Metrology," Phys. Rev.Lett. 96, p. 010401, 2006.
| Abstract category | Quantum Simulations |
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