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Chinese Physics B

Equivalent relation between quantum entanglement and steering in two-fermion spin systems under static magnetic fields

Xiao‐Gang Fan, Xin-Yu Yang, Wen‐Yang Sun, Cheng‐Cheng Liu, Zhi-Yong Ding, Juan He, Liu Ye

Published Feb 12, 2026• 0 citations
Publisher

Abstract

Abstract Quantum entanglement and steering are both fundamental concepts for describing quantum correlations, with steerable states forming a strict subset of entangled states. In general two-qubit systems, the relation between entanglement and steering can be characterized by an inequality, referred to as the constraint relation. In this work, we investigate a two-fermion spin system to explore the influence of static magnetic fields on quantum entanglement and steering. Our results demonstrate that entanglement and steering are equivalent in this system. The finding provides new perspectives for understanding quantum correlations in two-fermion spin systems. Furthermore, we examine the dynamic behavior of entanglement, showing that the maximum entanglement of this system affected by both external and internal factors.

DOI
10.1088/1674-1056/ae44f8

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Abstract Quantum entanglement and steering are both fundamental concepts for describing quantum correlations, with steerable states forming a strict subset of entangled states. In general two-qubit systems, the relation between entanglement and steering can be characterized by an inequality, referred to as the constraint relation. In this work, we investigate a two-fermion spin system to explore the influence of static magnetic fields on quantum entanglement and steering. Our results demonstrate that entanglement and steering are equivalent in this system. The finding provides new perspectives for understanding quantum correlations in two-fermion spin systems. Furthermore, we examine the dynamic behavior of entanglement, showing that the maximum entanglement of this system affected by both external and internal factors.
Abstract Entanglement and steering are used to describe quantum correlation. And steerable states form a strict subset of entangled states. A natural question arises concerning how much territory steerability occupies entanglement for a general two‐qubit entangled state. In this work, the constraint relation between steerability and concurrence is investigated by using two kinds of evolutionary states and any two‐qubit states (or lots of randomly generated states). By combining the theoretical and numerical proofs, the upper and lower boundaries of steerability are obtained. And the lower boundary can be used as a sufficient criterion for steering detection. Furthermore, a special kind of mixed state transformed by performing an arbitrary unitary transformation on Werner‐like state is considered, and a sufficient steering criterion described by concurrence and purity is proposed.
We investigate the behavior of quantum steering for a pair of quantum qubits described by the Heisenberg model with external magnetic field and in equilibrium with a reservoir at temperature T . Generally, the steerable weight, which is used to identify the steerability, is suppressed by thermal fluctuations. When the magnetic field is vanishing, the steerable weight behaves like the quantum entanglement. When the magnetic field is not zero, the steerable weight is dramatically different from the other quantities used to identify the quantum correlations between the two spins, i.e. , the concurrence, quantum discord and coherence. In the strong magnetic field limit, all of the other quantities we studied are vanishing for the Ising model, while steerable weight tends to one. This demonstrates that the strong transverse magnetic field is helpful to preserve the quantum steerability of the Ising model.
In this work, we study the quantum steering in two-qubit Heisenberg models with Dzyaloshinskii–Moriya (DM) interaction and an external magnetic field. We find that the steerable weight (SW) and the critical temperature where SW → 0 can be enhanced by the DM interactions. In the special case where the magnetic field is vanishing and the two spins are ferromagnetically coupled, the DM interaction can tune the zero-temperature SW from zero to a finite value. In addition to the SW, some other measurements used to identify the quantum entanglement and quantum correlations are investigated, i.e. , the concurrence, the quantum discord, and the robustness of coherence. In the strong magnetic field limit, our results show that the SW is dramatically different from the other measurements.
We consider the possibility of generation steerable states in Bose–Hubbard system composed of three interacting wells in the form of a triangle. We show that although our system still fulfills the monogamy relations, the presence of additional coupling which transforms a chain of wells onto triangle gives a variety of new possibilities for the generation of steerable quantum states. Deriving analytical formulas for the parameters describing steering and bipartite entanglement, we show that interplay between two couplings influences quantum correlations of various types. We compare the time evolution of steering parameters to those describing bipartite entanglement and find the relations between the appearance of maximal entanglement and disappearance of steering effect.
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Entanglement, quantum steering, and nonlocality are distinct quantum correlations which are the resources behind various quantum information and quantum computation applications. However, a central question of determining the precise quantitative relation among them is still unresolved. Here we present a mapping criterion between Bell nonlocality and quantum steering in the bipartite qudit-qubit system, as well as a mapping criterion between quantum steering and quantum entanglement in the bipartite qubit-qudit system, starting from the fundamental concepts of quantum correlations. Precise quantitative mapping criteria are derived analytically. Such mapping criteria are independent of the form of the state. In particular, they cover several previous well-known research results which are only special cases in our simple mapping criteria.