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Physica Scripta

Local quantum uncertainty in a two-qubit Heisenberg spin chain with intrinsic decoherence

You-neng Guo, Hu-Ping Peng, Qinglong Tian, Zhi-guang Tan, Ying Chen

Published Apr 23, 2021• 12 citations
Publisher

Abstract

Abstract Quantum correlation plays an important role in quantum information processing, for which various quantifiers have been proposed so far. In this paper, we address the dynamics of local quantum uncertainty (LQU) as a reliable quantifier of quantum correlation in a two-qubit Heisenberg spin chain in the presence of nonuniform external magnetic field and Dzyaloshinski-Moriya interaction with intrinsic decoherence. The influences of the initial states, external magnetic field strength, Dzyaloshinski-Moriya interaction strength and intrinsic decoherence rate on the dynamics of LQU have been in detail investigated. Our analytical results show that the dynamics of LQU is strongly depended on the form of initial states. For an initial correlated state, the dynamical behaviors of LQU exhibit either monotonic decay or damped oscillations with respect to time. While for an initial separable state, quantum correlation quantified by LQU can be created due to the Dzyaloshinski-Moriya interaction and Heisenberg anisotropic interaction. Besides, the relationship between LQU and l -norm coherence or concurrence is also demonstrated in the present model.

DOI
10.1088/1402-4896/abf960

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Abstract Quantum correlation plays an important role in quantum information processing, for which various quantifiers have been proposed so far. In this paper, we address the dynamics of local quantum uncertainty (LQU) as a reliable quantifier of quantum correlation in a two-qubit Heisenberg spin chain in the presence of nonuniform external magnetic field and Dzyaloshinski-Moriya interaction with intrinsic decoherence. The influences of the initial states, external magnetic field strength, Dzyaloshinski-Moriya interaction strength and intrinsic decoherence rate on the dynamics of LQU have been in detail investigated. Our analytical results show that the dynamics of LQU is strongly depended on the form of initial states. For an initial correlated state, the dynamical behaviors of LQU exhibit either monotonic decay or damped oscillations with respect to time. While for an initial separable state, quantum correlation quantified by LQU can be created due to the Dzyaloshinski-Moriya interaction and Heisenberg anisotropic interaction. Besides, the relationship between LQU and l -norm coherence or concurrence is also demonstrated in the present model.
In this paper, we investigate the pairwise quantum correlations in a two-qubit anisotropic Heisenberg model under the interplay of Calogero–Moser (CM) and Dzyaloshinsky–Moriya (DM) interactions in the presence of the homogeneous and inhomogeneous magnetic fields. We employ, respectively, the logarithmic negativity and local quantum uncertainty (LQU) to characterize the degree of entanglement and the amount of quantum correlations between the two parties of the considered system in equilibrium with a thermal reservoir. We analyze and compare the behaviors of the two quantum correlation quantifiers in the thermal state of the chain spin system and we discuss how relative distance between spins, equilibrium temperature, DM interaction coupling parameter and the external magnetic fields strengths influence the variations of both quantum correlation measures in such system.
Investigating the favorable configurations for non-classical correlations preservation has remained a hotly debated topic for the last decade. In this regard, we present a two-qubit Heisenberg spin chain system exposed to a time-dependent external magnetic field. The impact of various crucial parameters, such as initial strength and angular frequency of the external magnetic field along with the state’s purity and anisotropy of the spin-spin on the dynamical behavior of quantum correlations are considered. We utilize local quantum uncertainty (LQU) and quantum interferometric power (QIP) to investigate the dynamics of quantum correlations. We show that under the critical angular frequency of the external magnetic field and the spin-spin anisotropy, quantum correlations in the system can be successfully preserved. LQU and QIP suffer a drop as the interaction between the system and field is initiated, however, are quickly regained by the system. This tendency is confirmed by computing a measure of non-classical correlations according to the Clauser–Horne–Shimony–Holt inequality. Notably, the initial and final preserved levels of quantum correlations are only varied when variation is caused in the state’s purity.
Abstract This research delves into the dynamical behavior of quantum correlations and coherence within a mixed Heisenberg dimer system under the intrinsic decoherence. Our approach involves the application of logarithmic negativity, local quantum uncertainty, and the ℓ 1 norm-based coherence as quantifiers for entanglement, skew information correlations, and quantum coherence in this qubit-qutrit model. Our primary objective is to explore the impact of various factors on the dynamics of quantum correlations and quantum coherence. These factors encompass the initial density matrix and its mixing parameter, the intrinsic decoherence rate (γ), the external magnetic field, as well as intrinsic system parameters, notably the XXZ and uniaxial single-ion anisotropies. Our results demonstrate that the introduction of intrinsic decoherence (ID) significantly erodes quantum resources. Particularly, for high values of the ID rate (γ), excessive damping occurs, leading to the absence of oscillations or a rapid decay of quantum resources, ultimately stabilizing in steady states. Furthermore, the presence of an external homogeneous magnetic field further diminishes quantum resources within the system. However, despite the degradation induced by the combined influence of intrinsic decoherence and high external magnetic field intensities, the judicious selection of the initial density matrix and precise adjustment of the uniaxial single-ion anisotropy enable the preservation of quantum resources within the mixed spin-(1/2, 1) Heisenberg dimer.
Abstract In quantum information, it is important to recognize the effects of additional interactions, such as spin–orbit interactions, on the quantum information resources of two-qubit Heisenberg states. Therefore, we study the nonlocal correlation dynamics affected by the intrinsic decoherence of the spin–spin-Heisenberg-XYZ interaction, which is supported by spin–orbit interactions (Dzyaloshinsky–Moriya) of the x x and y y directions together. The two spins are coupled to an external inhomogeneous magnetic field (EIMF) in the x x -direction. We investigate and compare the nonclassical correlation dynamics of local quantum Fisher information, local quantum uncertainty, and log-negativity. The results show that spin–spin and spin–orbit interactions have a high capability to enhance non-local correlations in the presence of an external magnetic field. The enhanced non-local correlation can be further improved by strengthening the spin–spin and spin–orbit interactions, as well as by increasing the EIMF’s inhomogeneity and uniformity, which increases the amplitudes and fluctuations of the generated non-local correlation oscillations. The degradation of non-local correlations due to intrinsic decoherence can be controlled by spin–spin interactions. These degradation correlations can be enhanced by increasing the intensities of spin–orbit interactions, as well as by increasing the EIMF’s inhomogeneity and uniformity.
Generation and robustness of non-local correlations induced by Heisenberg XYZ and intrinsic decoherence models: (x,y)-spin-orbit interactions and xxx- magnetic field
In this work, the Milburn intrinsic decoherence model is used to investigate the role of spin-spin Heisenberg XYZ interaction supported by spin-orbit Dzyaloshinsky Moriya (DM) interactions of x and y directions together in the non-local correlation (NLC) dynamics of Local quantum Fisher information (LQFI), local quantum uncertainty (LQU), and Log-negativity's entanglement. The two-qubit Heisenberg XYZ (non-X) states' nonlocal correlation generations are explored under the effects of the uniformity and the inhomogeneity of an applied x-direction external inhomogeneous magnetic field (EIMF). Our meticulous exploration of the obtained results shows that the spin-spin Heisenberg XYZ and x,y-spin-orbit interactions have a high capability to raise non-local correlations in the presence of a weak external magnetic field. The raised non-local correlation can be improved by strengthening the spin-spin and x,y spin-orbit interactions and increasing the EIMF's inhomogeneity and uniformity. Non-local correlation oscillations' amplitudes and fluctuations are increased. The degradations of the NLCs' generations in the presence of intrinsic decoherence (NLCs' robustness against intrinsic decoherence) can be decreased by strengthening the spin-spin interactions. They can be increased by increasing the intensities of x,y spin-orbit interactions as well as increasing the EIMF's inhomogeneity and uniformity.
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.