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Chinese Physics B

Maximal and total skew information for a two-qubit system using nonlinear interaction models

Hong-Gui Sun, Wanfang Liu, Chunjie Li

Published Sep 1, 2011• 6 citations
Publisher

Abstract

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.

DOI
10.1088/1674-1056/20/9/090301

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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 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.
In terms of quantum Fisher information (QFI), a quantity χ 2 was introduced by Pezzé and Smerzi (Phys. Rev. Lett. 102 100401, 2009). They pointed out that the inequality χ 2<1 was a sufficient condition for multiparticle entanglement. For the two-qubit symmetric states, we found that the inequality χ 2<1 is a necessary and sufficient condition for entanglement and spin squeezing, and that χ 2 is equal to the second kind of spin squeezing parameter ξ22\xi _{2}^{2}ξ22​ . For the two-qubit asymmetric states, it is only a sufficient condition. In order to make it a necessary and sufficient condition, we extend the concept of the QFI and χ 2, and generalize the relations among the entanglement measurement, the spin squeezing parameters and χ 2 in symmetric pure states to arbitrary pure states.
The dynamics of entanglement of two superconducting charge qubit system interacting with a squeezed coherent state were examined by means of linear entropy. The influence of the relative phase of the two qubits' levels and squeezing parameter on the time evolution of linear entropy was discussed. The results showed that the linear entropy almost tends to zero at half the revival time when the two qubits were initially in the maximally entangled state. It was also showed that a greater number of oscillations of the linear entropy were observed with the increasing of squeezing parameter and the sustainment time of the maximum entropy was increased. There was no change in the maximum value of the linear entropy. Moreover,the relative phase of the two qubits' levels decreased the degree of entanglement between the two qubits and the field.
We introduce a new framework for quantum two-spin correlations based on a quantum skew information quantity and long-negativity. The quantum correlations for an anisotropic two-qubit Heisenberg [Formula: see text] model are affected by physical parameters such as intrinsic decoherence, Werner states and time-dependent magnetic fields. In particular, the joint effects of Werner states, magnetic fields and anisotropic parameters on quantum correlation robustness are investigated in the presence of intrinsic decoherence. For an initially uncorrelated state, robust entanglement is generated while skew information between the two quantum bits no longer exists. It is shown that the magnetic field makes the system strongly correlated with incredibly significant steady-state values in uncorrelated states. The phenomenon of sudden death and sudden birth appear during the evolution process of initial conditions. Finally, if the system starts from a mixed state or a Werner state, the magnetic field does not play a significant role in the monotonically decreasing correlations. By leveraging our framework, one can create a kind of stability between the uncertainty-induced quantum nonlocality and the local quantum uncertainty correlations.