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arXiv:2401.01063 · Physica Scripta

Trade-off relations of quantum resource theory in Heisenberg models

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

Published Apr 3, 2024• 9 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1088/1402-4896/ad3a45

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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.
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.
An analytical exploration of the phase decoherence equation of two qubits interacting with a coherent field with dipole–dipole interaction is introduced. The study examines the tradeoff relationships between intrinsic concurrence and first-order coherence in the qubits–cavity system while considering the impacts of decoherence and the interactions among the qubits. We affirm that the relationship between intrinsic concurrence and first-order coherence is valid. Additionally, we demonstrate that the minimum limit of intrinsic concurrence is universally applicable, although the upper limit is typically not. These connections in Heisenberg models can provide a means by which to investigate how quantum resources are allocated in spins, potentially leading to future applications in quantum information processing. It is partially but not completely possible to control the tradeoff relations between intrinsic concurrence and first-order coherence of the two-qubit cavity system; this control might involve actions that influence the system and are reflected in intrinsic concurrence and first-order coherence.
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.
Abstract Entanglement and coherence are deemed as two unreplaceable and important quantum resources in the regime of quantum physics, which are widely applied to quantum information processing and quantum computation. It is therefore natural to ask if there exists any intrinsic relationship between entanglement and coherence. In this work, the authors originally put forward tradeoff relations between intrinsic concurrence and first‐order coherence in the context of an arbitrary three‐qubit state. To do so, an equality relation related to the quantum entanglement and first‐order coherence for arbitrary three‐qubit pure states is derived first, and then extended to present another tradeoff relation regarding arbitrary three‐qubit states. Notably, physical explanation is offered for how coherence migrates in three‐qubit systems from first‐order coherence of a given subsystem to quantum correlations between subsystems. The result shows that the derived tradeoff relations can reveal the complementarity between intrinsic concurrence and first‐order coherence, which provides reliable theoretical basis of transformation and flow for quantum resources.
In this study, we investigate the impact of the XYZ-DM-Heisenberg model on quantum resources, including local quantum Fisher information, concurrence, and Jensen-Shannon coherence, in the presence of intrinsic decoherence. By exploring various spin-exchange interactions, with a focus on the role of the y-DM interaction, we reveal how these interactions affect quantum correlations and coherence dynamics. We find that the system transitions from separability to the generation of quantum properties when spin interactions are introduced. The specific parameter choices significantly influence the dynamic map of quantum functions. Notably, strong y-DM interaction, in combination with equal spin interaction, leads to pronounced fluctuations, while weak DM interaction results in sudden death and rebirth in the x direction. Additionally, ferro- and anti-ferromagnetic regimes impact the quantum functions differently. In the presence of intrinsic decoherence, fluctuations decrease, and coherence remains robust compared to the local quantum Fisher information and entanglement, reducing loss.