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Quantum Information Processing

Criticality, factorization and Wigner–Yanase skew information in quantum spin chains

W. W. Cheng, J. X. Li, Chuan-Jia Shan, Longyan Gong, Shengmei Zhao

Published May 4, 2015• 19 citations
Publisher
DOI
10.1007/s11128-015-1009-x

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\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
In this work, we address the ground-state properties of the anisotropic spin-1/2 Heisenberg XYZ chain under the interplay of magnetic fields and the Dzyaloshinskii-Moriya (DM) interaction which we interpret as an electric field. The identification of the regions of enhanced sensitivity determines criticality in this model. We calculate the Wigner-Yanase skew information (WYSI) as a coherence witness of an arbitrary two-qubit state under specific measurement bases. The WYSI is demonstrated to be a good indicator for detecting the quantum phase transitions. The finite-size scaling of coherence susceptibility is investigated. We find that the factorization line in the antiferromagnetic phase becomes the factorization volume in the gapless chiral phase induced by DM interactions, implied by the vanishing concurrence for a wide range of field. We also present the phase diagram of the model with three phases---antiferromagnetic, paramagnetic, and chiral---and point out a few common mistakes in deriving the correlation functions for the systems with broken reflection symmetry.
We study the effect of noise on the dynamics of the transverse-field Ising model quenched across a quantum critical point. To quantify two-spin correlations, we employ the quantum Fisher information (QFI) and the Wigner-Yanase skew information (WYSI) as measures of quantum coherence. In the noiseless case, in contrast to the dynamics of entanglement in anisotropic XY chains, both QFI and WYSI increase monotonically with the ramp quench time, approaching their adiabatic limits without exhibiting any Kibble-Zurek-type scaling with quench duration. In contrast, when noise is added to the quench protocol, the coherence dynamics change qualitatively: QFI and WYSI both decay exponentially with the timescale of a ramp quench, with an exponent determined by the noise intensity. Furthermore, the maximum ramp time, at which either of these measures reaches its maximum, scales linearly with the noise variance, featuring the same exponent that determines the optimal annealing time for minimizing defect production in noisy quantum annealing.