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Russian Microelectronics

Comparative Study of LQU and LQFI Measures of Quantum Correlations in Two-Spin-1/2 Heisenberg Systems

Mikhail A. Yurischev

Published Dec 1, 2023• 3 citations
Publisher

Abstract

Abstract Many measures of quantum correlations have been introduced so far, and now their properties are carefully studied both theoretically and experimentally. The most important among them are quantum entanglement and quantum discord. Recently, it was shown that the Wigner–Yanase skew information and quantum Fisher information also can serve as measures of nonclassical correlations. These discordlike measures are called local quantum uncertainty (LQU) and interferometric power or local quantum Fisher information (LQFI), correspondingly. In this paper the behavior of LQU and LQFI is considered at thermal equilibrium of the two-qubit Heisenberg models in the absence and presence of an external magnetic field; these cases correspond to the Bell-diagonal and general X states, respectively.

DOI
10.1134/s1063739723600176

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Abstract Many measures of quantum correlations have been introduced so far, and now their properties are carefully studied both theoretically and experimentally. The most important among them are quantum entanglement and quantum discord. Recently, it was shown that the Wigner–Yanase skew information and quantum Fisher information also can serve as measures of nonclassical correlations. These discordlike measures are called local quantum uncertainty (LQU) and interferometric power or local quantum Fisher information (LQFI), correspondingly. In this paper the behavior of LQU and LQFI is considered at thermal equilibrium of the two-qubit Heisenberg models in the absence and presence of an external magnetic field; these cases correspond to the Bell-diagonal and general X states, respectively.
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.
Abstract The thermal quantum correlations’ dynamics of an anisotropic two-qubit Heisenberg XYZ model in the presence of a x-projection external magnetic field are investigated in this paper. We use local quantum-Fisher information (LQFI), and log-negativity, and local quantum-uncertainty (LQU) to analyze the generated quantum correlation dynamics. Using the associated parameters, we demonstrate the successful generation of entanglement and quantum correlations beyond entanglement in the anisotropic spin-chain state. Certain values and ranges of anisotropy, external magnetic field, and spin coupling strength are proposed that can be used to achieve either a non-maximal or maximal quantum correlated state. The characterization of the spin-chain state by various parameters determines the dynamical patterns, degree, and preservation limits of the associated quantum correlations. Finally, the LQFI, LQU, and log-negativity functions’ robustness is highly dependent on their parameters, and they rarely agree on the degree of quantum correlations and dynamical patterns.
Abstract We employ entanglement negativity, local quantum uncertainty (LQU), and local quantum Fisher information (LQFI) to characterize thermal entanglement between two XYZ-Heisenberg-qubit states under the influence of Dzyaloshinsky-Moriya(DM) and Kaplan-Shekhtman-Entin-Wohlman-Aharony (KSEA) interactions, as well as a magnetic field and thermal equilibrium temperature. A comparative examination reveals similar behaviors among these correlation measures. For the antiferromagnetic scenario, we observe that increasing the DM interaction parameter D z enhances thermal entanglement. Conversely, in the ferromagnetic case, the behavior of thermal entanglement differs with varying D z . Additionally, employing Kraus operators, we explore the performance of these quantifiers under decoherence. Notably, LQFI exhibits greater robustness than negativity and LQU, even displaying a frozen phenomenon at some time under dephasing effects.
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.
Using Wigner–Yanase and Fisher information [including local quantum uncertainty (LQU) and local quantum Fisher information (LQFI)] as well as log-negativity, we investigate the thermal non-local correlations of two-qubit Heisenberg XYZ non-X states produced in the presence of the Dzyaloshinskii–Moriya (DM) interaction. The two-spin XYZ-Heisenberg non-local correlation decay can be weakened by increasing the DM interaction as well as the spin–spin XYZ-Heisenberg interactions. The LQFI correlation has greater resistance to thermal degradation. The spin–spin y-component antiferromagnetic coupling has a higher ability to protect the generated spin–spin nonlocal correlations against high temperatures. The emergence of the phenomena of the sudden death of log-negativity and the sudden change of the LQFI and LQU depend on the spin–spin XYZ-Heisenberg and DM interactions as well as on the bath temperature. The generated asymmetric correlations resulting due to the x,y-component spin interactions confirm that the antiferromagnetic coupling has a high ability to generate a maximally correlated two-qubit state. While the generated correlations, due to two-spin z-component interaction, present symmetric dynamics, and its amount depends on the x-component spin interaction.
Abstract Quantum Fisher information (QFI) and skew information (SI) plays a key role in the quantum resource theory. Understanding these measures in the physical system has practical significance in the state parameter estimation and quantum metrology. In this article, we consider a pair of spin-1/2 particles coupled with dipolar and Dzyaloshinsky-Moriya (DM) interactions, serving as the physical carrier of quantum information. We examine the bipartite nonlocal correlations of pair of spin-1/2 particle system for the thermal equilibrium states, characterized by local quantum uncertainty (LQU) and local quantum Fisher information (lQFI). The effects of dipolar coupling constants on quantum correlation quantifiers are studied. The DM interaction greatly enhances the quantum correlation in the system whereas the temperature tends to annihilate the amount of quantum correlations.