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Chinese Physics B

Maximal and total skew information of three-qubit system obtained using nonlinear interaction models

Hong-Gui Sun, Lihua Zhang, Wanfang Liu, Chunjie Li

Published Jan 1, 2012• 2 citations
Publisher

Abstract

Both the maximal and the total skew information have been studied. For a three-qubit system implemented in three nonlinear interaction models, we give the exact state vector at any time t . Based on this, we give the maximal and the total skew information. It is found that they have the same form and their evolution periods are dependent on the energy difference between the ground state and the second excited state in these models. The maximal skew information is always in the ( S x , S y ) plane. We give the condition for the occurrence of |GHZ〉 S y , in which they can reach the extreme values of 9/4 and 15/4, respectively. In three different decoherence channels, two kinds of information and the concurrence are calculated. We find that the phenomenon of the concurrence of sudden death occurs, but the above two kinds of information do not die suddenly. In the phase-damping channel, the two kinds of information will not be lost completely.

DOI
10.1088/1674-1056/21/1/010301

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Both the maximal and the total skew information have been studied. For a three-qubit system implemented in three nonlinear interaction models, we give the exact state vector at any time t . Based on this, we give the maximal and the total skew information. It is found that they have the same form and their evolution periods are dependent on the energy difference between the ground state and the second excited state in these models. The maximal skew information is always in the ( S x , S y ) plane. We give the condition for the occurrence of |GHZ〉 S y , in which they can reach the extreme values of 9/4 and 15/4, respectively. In three different decoherence channels, two kinds of information and the concurrence are calculated. We find that the phenomenon of the concurrence of sudden death occurs, but the above two kinds of information do not die suddenly. In the phase-damping channel, the two kinds of information will not be lost completely.
Maximal and total skew information is studied. For symmetric pure states of two-qubit, they are closely related to the linear entropy, the concurrence, and the spin squeezing parameter. For a two-qubit system implemented in three nonlinear interaction models with an external field, we give the exact state vectors and the expectation value 〈Sz〉 at any time t. Based on 〈Sz〉2, we give the maximal and the total skew information and a condition in which the maximal and the total skew information can reach 1 and 2, respectively.
The decay mechanism is considered in the one—axis twisting model and the two-countertwisting model for three-qubit system.Exact expression of the final states and the maximal Wigner-Yanse skew information(MSI) are given for different model within the Schrodinger picture.One can find that the MSI is always in the plane(S_x,S_y) Due to the decay mechanism and the nonlinear interaction,the MSI can be modulated and stored.We give the condition for occurrence of GHZ state,in which the MSI can reach the extreme values 9/4.
We give the explicit expressions of quantum Fisher information and skew information for a two-qubit Bell states. We investigate their dynamics under the decoherence effects: phase-damping channel, depolarizing channel and amplitude-damping channel. We also discuss the thermal entanglement quantified by Wootters concurrence for these three decoherence channels and we compare its dynamical behavior with the quantum Fisher information and skew information. We then use this comparison to investigate the influence of noisy channels on thermal entanglement and its role in boosting the performance of metrology protocols. It is shown that the correlations in two-qubit Bell states are more resistant to phase-damping channel and depolarizing channels.
We investigate the dynamics of quantum correlations [including skew information correlations beyond entanglement] of two isolated Su(2)-systems that are initially in a maximum Bell state or in a separable state. Each Su(2)-system is interacting with two-mode Su(1,1) coherent states. The time evolution of the density matrix of the two Su(2)-systems with the effect of intrinsic decoherence is analytically explored. The robustness of the initial quantum correlations for several initial coherence intensities, detunings, and intrinsic decoherences, is investigated. The robustness analysis of various correlation functions is based on the concurrence and quantum skew information. It is shown that the phenomena of sudden death and birth entanglement, and the sudden changes of local quantum uncertainty can be controlled. The correlations of the skew information present good robustness against the intrinsic decoherence and the detuning.
In this paper, we analyze the dynamics of non-local correlations (NLCs) in an anisotropic two-qubit Heisenberg XYZ model under the effect of the phase damping. An analytical solution is obtained by applying a method based on the eigenstates and the eigenvalues of the Hamiltonian. It is observed that the generated NLCs are controlled by the Dzyaloshinskii–Moriya interaction, the purity indicator, the interaction with the environment, and the anisotropy. Furthermore, it is found that the quantum correlations, as well as the sudden death and sudden birth phenomena, depend on the considered physical parameters. In particular, the system presents a special correlation: the skew-information correlation. The log-negativity and the uncertainty-induced non-locality exhibit the sudden-change behavior. The purity of the initial states plays a crucial role on the generated nonlocal correlations. These correlations are sensitive to the DM interaction, anisotropy, and phase damping.