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Journal of Atomic and Molecular Physics

Wigner-Yanse skew information of three-qubit system

Jiang Guang

Published Jan 1, 2012• 0 citations
OpenAlex

Abstract

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.

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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.
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 quantum-information theoretic notation of the Winger-Yanse skew information has been used to analyze the process of information transfer between probe fields and atomic ensemble in the electromagnetically induced transparency. It is well known that the skew information is a well-defined measure that quantifies the amount of the information a quantum state contains. We have calculated the dynamical skew information of the probe fields and the atomic ensemble, and found that the information for the individual atom is dependent of the numbers of the particles and the photons, as well as the state of the probe field. For a sufficiently weak coherent driving field, the dark-state polaritons is a purely atomic state with no photons in the composite system, and the information of the individual atom reaches the maximum value. However, the information of the probe field is not completely transferred into the atomic ensemble.
\n\nWe apply the Wigner-Yanase skew information approach to analyze two typical models that exhibit a topological quantum phase transition. Based on the exact solutions of the ground states, the Wigner-Yanase skew information between two nearest sites for each of the two models is obtained. For the one-dimensional Kitaev chain model, the first-order derivative of the Wigner-Yanase skew information is non-analytical around the critical point. The scaling behavior and the universality are verified numerically. In particular, the skew information can also detect the factorization transition in such a model. For the two-dimensional Kitaev honeycomb model, the first-order derivative of the Wigner-Yanase skew information shows some singularities at the critical points where the system transits from the gapless phase to the gapped one. Our results suggest that the Wigner-Yanase skew information can serve as a good indicator of the topological phase transitions in these models and shed considerable light on the relationships between topological quantum phase transition and information theory.\n
A family of skew information quantities is obtained, in which the well-known Wigner-Yanase skew information and quantum Fisher information stand as special cases. A transparent proof of convexity of the generalized skew information is given, implying a simple proof of the Wigner-Yanase-Dyson conjecture. We find in this work an exact skew information inequality for a qubit system, which may be regarded as the information counterpart of the uncertainty relation. A lower bound for the generalized skew information of a pair of incompatible observables in arbitrary dimension and also the upper bound for a qubit system are achieved.