Fidelity susceptibility and quantum Fisher information for density operators with arbitrary ranks

Liu, Jing; Xiong, Heng-Na; Song, Fei; Wang, Xiaoguang

doi:10.1016/j.physa.2014.05.028

Cited by 71 publications

(57 citation statements)

References 48 publications

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“…For non-full rank density matrix, the expression of the QFI F θ can be rewritten as [32,[38][39][40]]…”

Section: The Preliminariesmentioning

confidence: 99%

Local quantum uncertainty guarantees the measurement precision for two coupled two-level systems in non-Markovian environment

Zhang

2018

Annals of Physics

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Quantum Fisher information (QFI) is an important feature for the precision of quantum parameter estimation based on the quantum Cramér-Rao inequality. When the quantum state satisfies the von Neumann-Landau equation, the local quantum uncertainty (LQU), as a kind of quantum correlation, present in a bipartite mixed state guarantees a lower bound on QFI in the optimal phase estimation protocol [Phys. Rev. Lett. 110 (2013) 240402]. However, in the open quantum systems, there is not an explicit relation between LQU and QFI generally. In this paper, we study the relation between LQU and QFI in open systems which is composed of two interacting two-level systems coupled to independent non-Markovian environments with the entangled initial state embedded by a phase parameter θ. The analytical calculations show that the QFI does't depend on the phase parameter θ, and its decay can be restrained through enhancing the coupling strength or non-Markovianity. Meanwhile, the LQU is related to the phase parameter θ and shows plentiful phenomena. In particular, we find that the LQU can well bound the QFI when the coupling between the two systems is switched off or the initial state is Bell state.

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“…For non-full rank density matrix, the expression of the QFI F θ can be rewritten as [32,[38][39][40]]…”

Section: The Preliminariesmentioning

confidence: 99%

Local quantum uncertainty guarantees the measurement precision for two coupled two-level systems in non-Markovian environment

Zhang

2018

Annals of Physics

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“…In particular, Liu et al provided an analytical expression of the QFIM determined only by the support of the density matrix [61]. Based on the spectral decomposition of ρ(θ)…”

Section: Technical Preliminaries Of Qfimmentioning

confidence: 99%

Multiple phase estimation in quantum cloning machines

Yao

Xing

et al. 2014

Phys. Rev. A

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Since the initial discovery of the Wootters-Zurek no-cloning theorem, a wide variety of quantum cloning machines have been proposed aiming at imperfect but optimal cloning of quantum states within its own context. Remarkably, most previous studies have employed the Bures fidelity or the Hilbert-Schmidt norm as the figure of merit to characterize the quality of the corresponding cloning scenarios. However, in many situations, what we truly care about is the relevant information about certain parameters encoded in quantum states. In this work, we investigate the multiple phase estimation problem in the framework of quantum cloning machines, from the perspective of quantum Fisher information matrix (QFIM). Focusing on the generalized d-dimensional equatorial states, we obtain the analytical formulas of QFIM for both universal quantum cloning machine (UQCM) and phase-covariant quantum cloning machine (PQCM), and prove that PQCM indeed performs better than UQCM in terms of QFIM. We highlight that our method can be generalized to arbitrary cloning schemes where the fidelity between the single-copy input and output states is input-state independent. Furthermore, the attainability of the quantum Cramér-Rao bound is also explicitly discussed.

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“…Thus, C d−M is actually undefined here. However, since C d−M is also not involved in the calculation of QFI [22,23], therefore, it will not bring indeterminacy on the final expression of QFI. Based on this reason, we can simply take C d−M = 0 for convenience.…”

Section: Lyapunov Representationmentioning

confidence: 99%

“…Therefore, the QFI is actually the variance of SLD operator, i.e., F = ∆ 2 L , with ∆ 2 L := (L − L ) 2 . The SLD operator has been studied for years [19][20][21][22][23][24][25][26][27][28]. It is important for two reasons.…”

Section: Introductionmentioning

confidence: 99%

Quantum Fisher information and symmetric logarithmic derivative via anti-commutators

Liu

Chen

Jing

et al. 2016

J. Phys. A: Math. Theor.

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Abstract. Symmetric logarithmic derivative (SLD) is a key quantity to obtain quantum Fisher information (QFI) and to construct the corresponding optimal measurements. Here we develop a method to calculate the SLD and QFI via anticommutators. This method is originated from the Lyapunov representation and would be very useful for cases that the anti-commutators among the state and its partial derivative exhibits periodic properties. As an application, we discuss a class of states, whose squares linearly depend on the states themselves, and give the corresponding analytical expressions of SLD and QFI. A noisy scenario of this class of states is also considered and discussed. Finally, we readily apply the method to the block-diagonal states and the multi-parameter estimation scenarios.

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Fidelity susceptibility and quantum Fisher information for density operators with arbitrary ranks

Cited by 71 publications

References 48 publications

Local quantum uncertainty guarantees the measurement precision for two coupled two-level systems in non-Markovian environment

Local quantum uncertainty guarantees the measurement precision for two coupled two-level systems in non-Markovian environment

Multiple phase estimation in quantum cloning machines

Quantum Fisher information and symmetric logarithmic derivative via anti-commutators

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