We theoretically investigate quantum parameter estimation in a two-qubit anisotropic Heisenberg spin system with Dzyaloshinskii-Moriya (DM) interaction in the presence of intrinsic decoherence described by the Milburn model. Using the Quantum Fisher Information (QFI), we study the estimation of both the uniform magnetic field and the DM interaction strength. Analytical expressions for the time-evolved density matrix are obtained and used to explore the effects of exchange anisotropy, intrinsic decoherence, and probe-state preparation on the achievable estimation precision. Our results show that suitable tuning of the anisotropic exchange coupling and the initial entangled state can considerably enhance the estimation performance, with different optimal parameter regimes emerging for magnetic-field and DM-interaction sensing. To better understand the role of quantum resources in metrology, we also examine the behaviour of concurrence, quantum coherence, and von Neumann entropy. Overall, our findings demonstrate that anisotropic Heisenberg spin systems with DM interaction provide a promising and flexible platform for high-precision quantum metrology even in the presence of intrinsic decoherence.
By solving the Milburn equation, we investigate the properties of optimal channel capacity for the quantum dense coding via a two-qubit Heisenberg spin system with Dzyaloshinskii-Moriya (DM) interaction in the presence of intrinsic decoherence. The influences of different DM interactions, different initial states, anisotropic coupling parameters, and intrinsic decoherence on optimal coding capacity are analyzed in detail. It is found that the initial state of the system affects optimal coding capacity greatly, whose dependent parameters are not identical for different types of initial states. When the system is initially in the form of the nonmaximally entangled state cft| {01} ightangle + dft| {10} ightangle , a weak z-component DM interaction can enhance the value of optimal coding capacity as compared with the value without DM interaction, and the phase decoherence effect can suppress the oscillation of optimal coding capacity and make the capacity decrease to a stable value for the long-time evolution. It is also found that under the influence of intrinsic decoherence, the optimal transmission capacity of dense coding can keep an ideal maximal value of 2 by choosing the proper initial maximally entangled state. Moreover, no matter from which direction the DM interaction is introduced, the optimal coding capacity via the two-qubit Heisenberg spin system is always larger than the transmission capacity of any classical communication.
Taking the intrinsic decoherence effect into account, the entanglement of a two-qubit anisotropic Heisenberg XYZ chain in the presence of the Dzyaloshinski–Moriya (DM) anisotropic antisymetric interaction is investigated in this paper. Concurrence, the measurement of entanglement, is calculated. Compared with the anisotropic in XY plane, the DM interaction is another kind of anisotropic antisymmetric exchange interaction. It is shown that the intrinsic decoherence obviously suppresses the time evolution of the entanglement. The DM interaction only acts on the time evolution of the entanglement when the initial state is |ψ(0)⟩ = cosα|01⟩ + sinα|10⟩ and weakens the degree of entanglement. The anisotropic in XY plane merely impacts on the time evolution of the entanglement when the system is initially in a state |ψ(0)⟩ = cosα|00⟩ +sinα|11⟩. The sufficiently weak anisotropic in XY plane can effectively enhance the degree of entanglement.
Taking the intrinsic decoherence effect into account,the entanglement of a two-qubit anisotropic Heisenberg XYZ chain in the presence of the Dzyaloshinski-Moriya(DM)anisotropic antisymetric interaction is investigated in this paper.Concurrence,the measurement of entanglement,is calculated.Compared with the anisotropic in XY plane,the DM interaction is another kind of anisotropic antisymmetric exchange interaction.It is shown that the intrinsic decoherence obviously suppresses the time evolution of the entanglement.The DM interaction only acts on the time evolution of the entanglement when the initial state is |(?)(0)=cosα|01+sinα|10 and weakens the degree of entanglement.The anisotropic in XY plane merely impacts on the time evolution of the entanglement when the system is initially in a state |(?)(0)=cosα|00+sinα|11.The sufficiently weak anisotropic in XY plane can effectively enhance the degree of entanglement.
Entanglement is at the heart of quantum technologies such as quantum information and quantum metrology. Providing larger quantum Fisher information (QFI), entangled systems can be better resources than separable systems in quantum metrology. However the effects on the entanglement dynamics such as decoherence usually decrease the QFI considerably. On the other hand, Dzyaloshinskii-Moriya (DM) interaction has been shown to excite entanglement. Since an increase in entanglement does not imply an increase in QFI, and also there are cases where QFI decreases as entanglement increases, it is interesting to study the influence of DM interaction on quantum metrology. In this work, we study the QFI of thermal entanglement of two-qubit and three-qubit Heisenberg models with respect to SU(2) rotations. We show that even at high temperatures, DM interaction excites QFI of both ferromagnetic and antiferromagnetic models. We also show that QFI of the ferromagnetic model of two qubits can surpass the shot-noise limit of the separable states, while QFI of the antiferromagnetic model in consideration can only approach to the shot-noise limit. Our results open new insights in quantum metrology with Heisenberg models.
With considering the intrinsic decoherence, the dynamic behaviors of quantum entanglement in a three-qubit XXZ Heisenberg system with Dzyaloshinskii-Moriya (DM) interaction and anisotropy for different initial states are investigated. The research result shows that the anisotropy parameter does not affect the system entanglement, however, the intrinsic decoherence has obvious inhibitory effect on entanglement. When the initial state of system is an entangled state, we can obtain the stable value of entanglement by adjusting DM interaction parameters appropriately. As the system initial state is a separation state, entanglement oscillates, and the amplitude of oscillation decays with time periodically, and there will appear the death phenomenon after each oscillation, and with time going on, its concurrence will be zero. When the initial state is entangled, by choosing the proper DM parameter, the three pairs of entanglements oscillate with time and eventually approach to a steady value. The increase of accelerates the decay of concurrence. When the initial state is separated, entanglement oscillates, and the amplitude of oscillation decays with time periodically, and there will appear the death phenomenon after each oscillation, with time going on, its concurrence will be zero. Therefore, the proper initial state and DM interaction parameters can control the concurrence effectively under the intrinsic decoherence, thereby obtaining the preferable entanglement resource.
We study thermal quantum correlations and coherence in Heisenberg
XY model with anisotropic interactions under a uniform magnetic field $ B $. Using concurrence
C, local quantum uncertainty (LQU), Bell-Clauser-Horne-Shimony-Holt (CHSH) nonlocality $ \mathbb{B}$, and coherence
Cl as quantifiers, we analyze how magnetic anisotropy $ δ_m $, coupling anisotropy $ δ_c $, Dzyaloshinskii-Moriya (DM) interaction $ D $, temperature $ T $, and magnetic field $ B $ modulate quantum resources. At low temperatures and relevant magnetic fields, the entanglement is maximized, but exhibits sudden death for $ δ_m = 0 $, which turns into a smooth decay as $ δ_m $ increases, highlighting its stabilizing role. LQU shows that stronger anisotropy suppresses quantum correlations, while $ \mathbb{B} $ induces a non-monotonic response peaking at a critical field $ B_c
.Bell−CHSHnonlocalityviolations( \mathbb{B} > 2 $) persist below $ B_c
,butthermalnoise( T \geq 1 $) suppresses them. Coherence $ C_l $ is most robust to thermal fluctuations, especially for high
δm, which also dampens abrupt quantum phase transitions. The DM interaction is essential for entanglement generation, with $ D $ and anisotropy synergistically enhancing correlation resilience. We identify a hierarchy of thermal degradation: nonlocality ($ \mathbb{B}
)vanishesfirst,followedbyentanglement( C $), then general quantum correlations (LQU), while coherence $ C_l $ persists the longest. These results demonstrate tunable control of quantum resources via anisotropy and external parameters, providing insights for the design of robust spin-based quantum technologies.