Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Alexandria Engineering Journal

Trade-off relations between two-qubit coherence and intrinsic concurrence for Heisenberg XYZ states induced by intrinsic decoherence model

Fahad Aljuaydi

Published Feb 6, 2025• 12 citations
Publisher

Abstract

This work investigates the trade-off relations between intrinsic concurrence, concurrence, first-order coherence, and total purity for generated two-qubit Heisenberg XYZ states due to spin–spin interactions supported by spin–orbit interactions in the x and y directions with an external inhomogeneous magnetic field in the x direction by using the Milburn model of intrinsic decoherence. We apply the complementary trade-off relations between quantum resource quantifiers when the two-spin Heisenberg XYZ interactions start with a maximally pure state ( | 1 A 〉 ⊗ | 1 B 〉 ) and a maximally entangled state ( 1 2 [ | 1 A 〉 ⊗ | 1 B 〉 + | 0 A 〉 ⊗ | 0 B 〉 ] ) . The results of the trade-off relations provide a reliable theoretical basis for the mutual transformation between quantum resource quantifiers. It is shown that the spin–spin-Heisenberg XYZ and x , y -spin–orbit interactions have a high capability to generate entanglement and degrade coherence with oscillatory evolutions. The amplitudes and frequencies of the oscillations of the information resources depend on the increase of the applied external inhomogeneous magnetic field, the spin–orbit interactions, and the intrinsic two-spin decoherence. It is found that the stationary quantum information resources generated by intrinsic decoherence depend on the spin–spin, spin–orbit interactions as well as on the applied external inhomogeneous magnetic field in the x -direction.

DOI
10.1016/j.aej.2025.01.106

Related papers

Generation and robustness of non-local correlations induced by Heisenberg XYZ and intrinsic decoherence models: (x,y)-spin-orbit interactions and $x$- magnetic field

Fahad Aljuaydi, Sultan Almutairi, A.‐B. A. Mohamed

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.

arXiv:2405.17157•May 27, 2024•0 citations

Nonclassical correlation dynamics of Heisenberg XYZ states with ( x, y )-spin--orbit interaction, x -magnetic field, and intrinsic decoherence effects

Fahad Aljuaydi, Sattam N. Almutairi, Heba Allhibi +1 more

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.

Open Physics•Jan 1, 2025•1 citation

Trade-off relations of quantum resource theory in Heisenberg models

Asad Ali, Saif M. Al-Kuwari, Saeed Haddadi

Abstract Studying the relations between entanglement and coherence is essential in many quantum information applications. For this, we consider the concurrence, intrinsic concurrence and first-order coherence, and evaluate the proposed trade-off relations between them. In particular, we study the temporal evolution of a general two-qubit XYZ Heisenberg model with asymmetric spin-orbit interaction under decoherence and analyze the trade-off relations of quantum resource theory. For XYZ Heisenberg model, we confirm that the trade-off relation between intrinsic concurrence and first-order coherence holds. Furthermore, we show that the lower bound of intrinsic concurrence is universally valid, but the upper bound is generally not. These relations in Heisenberg models can provide a way to explore how quantum resources are distributed in spins, which may inspire future applications in quantum information processing.

arXiv:2401.01063•Physica Scripta•Apr 3, 2024•9 citations

Dynamics of trade-off relations between quantum information resources in two qubits interacting individually and nonlinearly with a cavity: Decoherence model

Fahad Aljuaydi, A-B A Mohamed, Mostafa Hashem

The dynamics of trade-off relations between quantum information resources are investigated in a system of two non-interacting qubits, each individually and nonlinearly coupled to coherent cavity fields through intensity-dependent coupling. The qubits are initially prepared in a maximally entangled Bell state, while the cavity fields are assumed to be in coherent states. An exact analytical treatment of the reduced two-qubit density matrix is presented under qubit–cavity detuning and intrinsic decoherence governed by the Milburn model. The time evolutions of first-order coherence, concurrence, intrinsic concurrence and purity are analyzed to elucidate the redistribution of quantum resources. The results confirm that intrinsic concurrence and first-order coherence obey a complementary trade-off relation governed by the purity of the two-qubit state, with standard concurrence acting as a lower bound for intrinsic concurrence throughout the dynamics. The roles of the initial coherent field intensity, qubit–cavity detuning and intrinsic decoherence are examined, showing that nonlinear atom–cavity interactions induce regular oscillatory behavior accompanied by entanglement sudden death and revival phenomena. Increasing the coherent field intensity enhances coherence generation and accelerates entanglement degradation of the generated two-qubit states.

Modern Physics Letters A•Feb 6, 2026•0 citations

Universal trade-off relation between coherence and intrinsic concurrence for two-qubit states

Xiao‐Gang Fan, Wen‐Yang Sun, Zhiyong Ding +4 more

Entanglement and coherence are two essential quantum resources for quantum information processing. A natural question arises of whether there are direct link between them. And by thinking about this question, we propose a new measure for quantum state that contains concurrence and is called intrinsic concurrence. Interestingly, we discover that the intrinsic concurrence is always complementary to coherence. Note that the intrinsic concurrence is related to the concurrence of a special pure state ensemble. In order to explain the trade-off relation more intuitively, we apply it in some composite systems composed by a single-qubit state coupling four typical noise channels with the aim at illustrating their mutual transformation relationship between their coherence and intrinsic concurrence. This unified trade-off relation will provide more flexibility in exploiting one resource to perform quantum tasks and also provide credible theoretical basis for the interconversion of the two important quantum resources.

arXiv:1904.01386•Apr 2, 2019•0 citations

Intrinsic decoherence effects on nonclassical correlations in a symmetric spin–orbit model

Abdel‐Baset A. Mohamed, Ahmad N. Khedr, Saeed Haddadi +3 more

Nonclassical correlations dynamics of local quantum Fisher information, trace-norm measurement-induced nonlocality, and log-negativity are investigated in a symmetric spin–orbit model. This model is described by a Heisenberg XYZ two-spin system exposed to the magnetic field and Kaplan–Shekhtman–Entin-Wohlman–Aharony (KSEA) interaction under the intrinsic decoherence effects. To evaluate the resourcefulness of this model for the generation and preservation of quantum correlations, we consider two qubits that are initially prepared in two different states, namely uncorrelated and maximally correlated states. The magnetic field is discovered to be effective at generating and preserving nonclassical correlations. Besides, we find that the KSEA interaction can alter the generation, preservation, and revival features of nonclassical correlations in the two-qubit system. However, the bipartite nonclassical correlations become extremely fragile when intrinsic decoherence effects appear.

Results in Physics•Jun 10, 2022•38 citations
This work investigates the trade-off relations between intrinsic concurrence, concurrence, first-order coherence, and total purity for generated two-qubit Heisenberg XYZ states due to spin–spin interactions supported by spin–orbit interactions in the x and y directions with an external inhomogeneous magnetic field in the x direction by using the Milburn model of intrinsic decoherence. We apply the complementary trade-off relations between quantum resource quantifiers when the two-spin Heisenberg XYZ interactions start with a maximally pure state ( | 1 A 〉 ⊗ | 1 B 〉 ) and a maximally entangled state ( 1 2 [ | 1 A 〉 ⊗ | 1 B 〉 + | 0 A 〉 ⊗ | 0 B 〉 ] ) . The results of the trade-off relations provide a reliable theoretical basis for the mutual transformation between quantum resource quantifiers. It is shown that the spin–spin-Heisenberg XYZ and x , y -spin–orbit interactions have a high capability to generate entanglement and degrade coherence with oscillatory evolutions. The amplitudes and frequencies of the oscillations of the information resources depend on the increase of the applied external inhomogeneous magnetic field, the spin–orbit interactions, and the intrinsic two-spin decoherence. It is found that the stationary quantum information resources generated by intrinsic decoherence depend on the spin–spin, spin–orbit interactions as well as on the applied external inhomogeneous magnetic field in the x -direction.
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 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.
Abstract Studying the relations between entanglement and coherence is essential in many quantum information applications. For this, we consider the concurrence, intrinsic concurrence and first-order coherence, and evaluate the proposed trade-off relations between them. In particular, we study the temporal evolution of a general two-qubit XYZ Heisenberg model with asymmetric spin-orbit interaction under decoherence and analyze the trade-off relations of quantum resource theory. For XYZ Heisenberg model, we confirm that the trade-off relation between intrinsic concurrence and first-order coherence holds. Furthermore, we show that the lower bound of intrinsic concurrence is universally valid, but the upper bound is generally not. These relations in Heisenberg models can provide a way to explore how quantum resources are distributed in spins, which may inspire future applications in quantum information processing.
The dynamics of trade-off relations between quantum information resources are investigated in a system of two non-interacting qubits, each individually and nonlinearly coupled to coherent cavity fields through intensity-dependent coupling. The qubits are initially prepared in a maximally entangled Bell state, while the cavity fields are assumed to be in coherent states. An exact analytical treatment of the reduced two-qubit density matrix is presented under qubit–cavity detuning and intrinsic decoherence governed by the Milburn model. The time evolutions of first-order coherence, concurrence, intrinsic concurrence and purity are analyzed to elucidate the redistribution of quantum resources. The results confirm that intrinsic concurrence and first-order coherence obey a complementary trade-off relation governed by the purity of the two-qubit state, with standard concurrence acting as a lower bound for intrinsic concurrence throughout the dynamics. The roles of the initial coherent field intensity, qubit–cavity detuning and intrinsic decoherence are examined, showing that nonlinear atom–cavity interactions induce regular oscillatory behavior accompanied by entanglement sudden death and revival phenomena. Increasing the coherent field intensity enhances coherence generation and accelerates entanglement degradation of the generated two-qubit states.
Entanglement and coherence are two essential quantum resources for quantum information processing. A natural question arises of whether there are direct link between them. And by thinking about this question, we propose a new measure for quantum state that contains concurrence and is called intrinsic concurrence. Interestingly, we discover that the intrinsic concurrence is always complementary to coherence. Note that the intrinsic concurrence is related to the concurrence of a special pure state ensemble. In order to explain the trade-off relation more intuitively, we apply it in some composite systems composed by a single-qubit state coupling four typical noise channels with the aim at illustrating their mutual transformation relationship between their coherence and intrinsic concurrence. This unified trade-off relation will provide more flexibility in exploiting one resource to perform quantum tasks and also provide credible theoretical basis for the interconversion of the two important quantum resources.
Nonclassical correlations dynamics of local quantum Fisher information, trace-norm measurement-induced nonlocality, and log-negativity are investigated in a symmetric spin–orbit model. This model is described by a Heisenberg XYZ two-spin system exposed to the magnetic field and Kaplan–Shekhtman–Entin-Wohlman–Aharony (KSEA) interaction under the intrinsic decoherence effects. To evaluate the resourcefulness of this model for the generation and preservation of quantum correlations, we consider two qubits that are initially prepared in two different states, namely uncorrelated and maximally correlated states. The magnetic field is discovered to be effective at generating and preserving nonclassical correlations. Besides, we find that the KSEA interaction can alter the generation, preservation, and revival features of nonclassical correlations in the two-qubit system. However, the bipartite nonclassical correlations become extremely fragile when intrinsic decoherence effects appear.