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Acta Physica Sinica

Effects of Dzyaloshinskii-Moriya interaction and intrinsic decoherence on quantum dense coding via a two-qubit Heisenberg spin system

Zou Qin, Hu Xiao-Mian, Liu Jin-Ming

Published Jan 1, 2015• 5 citations
Publisher

Abstract

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.

DOI
10.7498/aps.64.080302

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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.
We investigate the joint effects of phase decoherence, Dzyaloshinskii-Moriya (DM) interaction and inhomogeneity of the external magnetic field ( b ) on dense coding in a two-qubit anisotropic Heisenberg XYZ spin chain. Analytical expressions are obtained for the dense coding capacity. It is found that valid dense coding is always possible with this model when the system is initially prepared in the maximum entangled state. Moreover, optimal dense coding can be implemented for this initial state as long as the mean spin-spin coupling constant J + of the XY plane is larger than b and the DM interaction despite the intrinsic decoherence. Non-maximal entangled initial states are found to be undesirable for dense coding with this model.
We investigate the effects of different components of the Dzyaloshinskii—Moriya (DM) anisotropic antisymmetric interaction on optimal dense coding with a two-qubit Heisenberg XXZ chain in the presence and in the absence of external magnetic fields. The anisotropic coupling parameter Δ, isotropic coupling parameter J , and the DM interaction parameters are found to be effective for optimal dense coding, while the magnetic field turns out to be destructive. Moreover, the results show that the case of antiferromagnetic (AFM) is more ideal for optimal dense coding than the case of ferromagnetic (FM) in general. In the case of AFM, by comparison of the two cases with the same fixed x - and z -component parameters of DM interaction ( D x and D z ), the appropriate model for optimal dense coding is indicated for the different value intervals of Δ. Comparison of the effects of D z and D x on optimal dense coding is made and their dominant regions are clarified.
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 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.
Using the Milburn equation, we have studied the properties of the entanglement and fidelity dynamics in a spin system with different Dzyaloshinskii-Moriya interaction and magnetic field in detail. Effects of different Dzyaloshinskii-Moriya interaction, different magnetic fields, and the initial states on the entanglement and fidelity are discussed. Results show that entanglement decoherence can be suppressed by inhomogeneous magnetic fields. Initial state affects greatly the entanglement, and a proper entanglement can be obtained by adjusting the directions of Dzyaloshinskii-Moriya interaction. For a particular initial state, an optimal fidelity is obtained by changing the direction of the Dzyaloshinskii-Moriya interaction. Moreover, no matter how homogeneous or inhomogeneous the magnetic fields are, they cannot enhance the fidelity. The dependence of entanglement and fidelity on the angle of initial state shows periodicity. Hence we can select an optimal initial state for a specific condition according to requirement.