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International Journal of Theoretical Physics

Storage of Maximal Wigner-Yanase Skew Information of Two-Qubit System Using Nonlinear Interactions with Decay

Wanfang Liu, Xun-Chang Yin, Li-Hua Zhang

Published Jun 23, 2011• 11 citations
Publisher

Abstract

The decay mechanism is considered in some nonlinear interaction models for two-qubit system. Exact expression of the final states of two-qubit are given for different model. We find that the maximal Wigner-Yanase skew information can be modulated and stored via using decay mechanism and nonlinear interaction. Due to the maximal Wigner-Yanase skew information being equivalent to the concurrence, the conditions of generating the maximally entangled state (i.e., the Bell state) are obtained.

DOI
10.1007/s10773-011-0842-7

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The decay mechanism is considered in some nonlinear interaction models for two-qubit system. Exact expression of the final states of two-qubit are given for different model. We find that the maximal Wigner-Yanase skew information can be modulated and stored via using decay mechanism and nonlinear interaction. Due to the maximal Wigner-Yanase skew information being equivalent to the concurrence, the conditions of generating the maximally entangled state (i.e., the Bell state) are obtained.
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.
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.
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.
The change of the total Wigner-Yanase skew information of two coupled two-level atoms interacting with two-mode squeezed vacuum state field was investigated. The results showed that when the squeezed factor was smaller,the interaction between atoms and field,the dipole-dipole interaction of two atoms determined evolution period of the total Wigner-Yanase skew information together; enhancing the dipoledipole interaction of two atoms could resist the loss of the total Wigner-Yanase skew information; the squeezed factor of light field played an important role in the loss of the total Wigner-Yanase skew information,and when the squeezed factor was bigger,the total Wigner-Yanase skew information of atoms would lose completely.
A Bell-type inequality is proposed in terms of Wigner-Yanase skew information, which is quadratic and involves only one local spin observable at each site. This inequality presents a hierarchic classification of all states of multipartite quantum systems from separable to fully entangled states, which is more powerful than the one presented by quadratic Bell inequalities from two-entangled to fully entangled states. In particular, it is proved that the inequality provides an exact test to distinguish entangled from nonentangled pure states of two qubits. Our inequality sheds considerable light on relationships between quantum entanglement and information theory.