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arXiv:2110.09427 · Journal of the Optical Society of America B

Enhancing the estimation precision of an unknown phase shift in multipartite Glauber coherent states via skew information correlations and local quantum Fisher information

Mehdi El Bakraoui, Abdallah Slaoui, Hanane El Hadfi, Mohammed Daoud A

Published Mar 16, 2022• 18 citations
arXivHTMLPDF

Abstract

Local quantum uncertainty (LQU) and local quantum Fisher information (LQFI) are both tools used to capture purely quantum correlations in multipartite quantum systems. In this paper, we study these quantifiers in the case of multipartite Glauber coherent states, which include the Greenberger–Horne–Zeilinger and Werner states. We perform a comparative study between LQFI and LQU in an isolated system. By using the Kraus operator representation, we study the behavior of these quantifiers on the dephasing channel to investigate their performances under the decoherence effect. In addition, the robustness to the decoherence effect of these two quantifiers is studied. We further examine the situation involving the multipartite Glauber coherent state to decide the sensitivity of the probe state as a resource for quantum estimation protocols.

DOI
10.1364/josab.446354

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We derive the compact closed forms of local quantum uncertainty (LQU) and local quantum Fisher information (LQFI) for hybrid qubit-qutrit axially symmetric (AS) states. This allows us to study the quantum correlations in detail and present some essentially novel results for spin-(1/2, 1) systems, the Hamiltonian of which contains ten independent types of physically important parameters. As an application of the derived formulas, we study the behavior of these two quantum correlation measures at thermal equilibrium. New features are observed in their behavior that are important for quantum information processing. Specifically, cascades of sudden changes in the behavior of LQU and LQFI are found with a smooth change in temperature or interaction parameters. Interestingly, in some cases, sudden transitions are observed in the behavior of LQU but not in LQFI, and vice versa. Moreover, our compact formulas open a way to apply them to other problems, for instance, when investigating the environmental effects on quantum correlations in open systems.
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Abstract Quantum correlations play an important role in quantum information theory. Quantum Fisher information (QFI) via local observables and via local measurements (i.e. local QFI (LQFI)) is a fundamental concept in quantum estimation and quantum metrology. LQFI captures the quantumness of correlations in a multicomponent quantum system. This new discord-like measure is very similar to the quantum correlations measure called local quantum uncertainty (LQU). In this work we will study the LQFI and the LQU in the two-qubit Heisenberg XYZ spin chain model with Dzyaloshinskii–Moriya (DM) interaction in the z -direction. Here we show that the DM interaction and spin interactions along the x - and z -axes can increase and maintain LQFI and LQU. It is also shown that because of thermal fluctuations LQFI and LQU are decreased by increasing temperature. They are equal to one at very low temperature and start to decay only after a thereshold temperature.
Quantum Fisher information of a parameter characterizes the sensitivity of the state with respect to changes of the parameter. In this article, we study the quantum Fisher information of a state with respect to SU(2)\mathrm{SU}(2)SU(2) rotations under three decoherence channels: the amplitude-damping, phase-damping, and depolarizing channels. The initial state is chosen to be a Greenberger-Horne-Zeilinger state of which the phase sensitivity can achieve the Heisenberg limit. By using the Kraus operator representation, the quantum Fisher information is obtained analytically. We observe the decay and sudden change of the quantum Fisher information in all three channels.