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arXiv:2506.03879 · Laser Physics Letters

Exploring entanglement, Wigner negativity and Bell nonlocality for anisotropic two-qutrit states

Huan Liu, Zu-wu Chen, Xue-feng Zhan, H Yuan, Xue-xiang Xu

Published Nov 1, 2025• 0 citations
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Abstract

Abstract We introduce a family of anisotropic two-qutrit states (AITTSs). These AITTSs are expressed as ρ aiso = p | ψ ( θ , ϕ ) ⟩ ⟨ ψ ( θ , ϕ ) | + ( 1 − p ) I 9 9 with | ψ ( θ , ϕ ) ⟩ = sin ⁡ θ cos ⁡ ϕ | 00 ⟩ + sin ⁡ θ sin ⁡ ϕ | 11 ⟩ + cos ⁡ θ | 22 ⟩ and I 9 = ∑ j , k = 0 2 | j k ⟩ ⟨ j k | . For a given p ∈ [ 0 , 1 ] , these states are adjustable in different ( θ , ϕ ) directions. In the case of ( θ , ϕ

DOI
10.1088/1612-202x/ae18bc

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Abstract We introduce a family of anisotropic two-qutrit states (AITTSs). These AITTSs are expressed as ρ aiso = p | ψ ( θ , ϕ ) ⟩ ⟨ ψ ( θ , ϕ ) | + ( 1 − p ) I 9 9 with | ψ ( θ , ϕ ) ⟩ = sin ⁡ θ cos ⁡ ϕ | 00 ⟩ + sin ⁡ θ sin ⁡ ϕ | 11 ⟩ + cos ⁡ θ | 22 ⟩ and I 9 = ∑ j , k = 0 2 | j k ⟩ ⟨ j k | . For a given p ∈ [ 0 , 1 ] , these states are adjustable in different ( θ , ϕ ) directions. In the case of ( θ , ϕ
Quantum entanglement and quantum nonlocality of N -photon entangled states |ψ Nm ⟩ = C m [cos γ| N − m ⟩ 1 | m ⟩ 2 +e iθ m sin γ| m ⟩ 1 | N − m ⟩ 2 ] and their superpositions are studied. We point out that the relative phase θ m affects the quantum nonlocality but not the quantum entanglement for the state |ψ Nm ⟩. We show that quantum nonlocality can be controlled and manipulated by adjusting the state parameters of |ψ Nm ⟩, superposition coefficients and the azimuthal angles of the Bell operator. We also show that the violation of the Bell inequality can reach its maximal value under certain conditions. It is found that quantum superpositions based on |ψ Nm ⟩ can increase the amount of entanglement and give more ways to reach the maximal violation of the Bell inequality.
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考虑内在的 decoherence 效果， two-qubit 的纠纷各向异性的 Heisenberg XYZ 链面对 Dzyaloshinski Moriya (DM ) ，各向异性的 antisymetric 相互作用在这篇论文被调查。同时发生，纠纷的测量，被计算。与相比在 XY 飞机各向异性， DM 相互作用是另一种各向异性的反对称的交换相互作用。内在的 decoherence 显然压制纠纷的时间进化，这被显示出。当起始的状态是 |ψ (0 )= cosα|01 + sinα|10 并且削弱纠纷的度时， DM 相互作用仅仅对纠纷的时间进化起作用。在当系统开始在州的 |ψ (0 ) 时，飞机仅仅在纠纷的时间进化上影响的 XY 各向异性 = cosα|00 +sin α|11。足够地弱在飞机能有效地提高的 XY 各向异性纠纷的度。
This paper investigates the entanglement evolution of a two-qubit anisotropic Heisenberg XYZ chain in the presence of Dzyaloshinskii–Moriya interaction. The time evolution of the concurrence is studied for the initial pure entangled states cos θ |00⟩ + sin θ |11⟩ and cos φ |01⟩ + sin φ |10⟩ at zero temperature. The influences of Dzyaloshinskii–Moriya interaction D , anisotropic parameter Δ and environment coupling strength γ on entanglement evolution are analysed in detail. It is found that the effect of noisy environment obviously suppresses the entanglement evolution, and the Dzyaloshinskii–Moriya interaction D acts on the time evolution of entanglement only when the initial state is cos φ |01⟩ + sin φ |10⟩. Finally, a formula of steady state concurrence is obtained, and it is shown that the stable concurrence, which is independent of different initial states and Dzyaloshinskii–Moriya interaction D , depends on the anisotropic parameter Δ and the environment coupling strength γ.
Bound entanglement, being entangled yet not distillable, is essential to our understanding of the relations between nonlocality and entanglement besides its applications in certain quantum information tasks. Recently, bound entangled states that violate a Bell inequality have been constructed for a two-qutrit system, disproving a conjecture by Peres that bound entanglement is local. Here we construct this kind of nonlocal bound entangled state for all finite dimensions larger than two, making possible their experimental demonstration in most general systems. We propose a Bell inequality, based on a Hardy-type argument for nonlocality, and a steering inequality to identify their nonlocality. We also provide a family of entanglement witnesses to detect their entanglement beyond the Bell inequality and the steering inequality.