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arXiv:quant-ph/0602143 · Quantum Information Processing

A Characterization of Global Entanglement

Peter J. Love, Alec Maassen van den Brink, Anatoly Yu. Smirnov, M. H. S. Amin, M. Grajcar, Evgeni V. Il’ichev, A. Izmalkov, Alexandre M. Zagoskin

Published May 14, 2007• 87 citations
arXivHTMLPDF
DOI
10.1007/s11128-007-0052-7

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A Perspective on Quantum Entanglements

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We investigate global entanglement in the ground state of single-molecular magnet Na 9 [Cu 3 Na 3 (H 2 O) 9 (α-AsW 9 O 33 ) 2 ]·26H 2 O with an external magnetic field. The concurrence, tangle, and measure function Q , which characterize the pairwise entanglement, 3-party entanglement and total entanglement, respectively, are calculated numerically at zero temperature. The results show that the magnitude and direction of the applied magnetic field play a significant role in the properties of three kinds of entanglement measures. We give a physical interpretation of the variation of the global entanglement with the magnetic field. Finally, the phase diagram of the global entanglement characterized by the critical magnetic fields is presented.
Entanglement is known as an important indicator for characterizing different types of quantum phase transitions (QPTs); however, it faces some challenges in the Kosterlitz-Thouless (KT) phase transitions due to an essential singularity which cannot be identified in finite derivatives of the ground-state energy. In this paper, we consider global entanglement (GE) in a KT phase transition and show that while it does not indicate any clear signature of the phase transition, the conditional version of GE is a good indicator with strong signatures of the KT transition. In particular, we study a deformed version of the Zd{Z}_{d}Zd​ Kitaev model which has an intermediate KT phase which separates a Zd{Z}_{d}Zd​ topological phase from a magnetized phase at two different KT transition points. Using a mapping to the classical ddd-state clock model, we consider GE and the generalized GE and show that they do not provide a reliable indicator of transition points. However, their difference, called conditional global entanglement (QQQ), shows a peak at the first KT transition point. Additionally, we show that it can characterize various phases of the model as it behaves substantially differently in each phase. We therefore conclude that QQQ is a useful measure that can characterize various phases of KT QPTs as well as their related critical points.