Sumiyoshi Abe
College of Information Science and Engineering, Huaqiao University, Xiamen, 361021 China
Mie University, Tsu, 514-8507 Japan
Kazan Federal University, Kazan, 420008 Russia
For citation: Abe S. Estimating entanglement in a class of N-qudit states. Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 2018, vol. 160, no. 2, pp. 213–219.
Для цитирования: Abe S. Estimating entanglement in a class of N-qudit states // Учен. зап. Казан. ун-та. Сер. Физ.-матем. науки. – 2018. – Т. 160, кн. 2. – С. 213–219.
Abstract
The logarithmic derivative (or quantum score) of a positive definite density matrix appearing in the quantum Fisher information has been discussed, and its exact expression has been presented. The problem of estimating the parameters in a class of the Werner-type N-qudit states has been studied in the context of the quantum Cramer–Rao inequality. The largest value of the lower bound to the error of estimate by the quantum Fisher information has been shown to coincide with the separability point only in the case of two qubits. It has been found, on the other hand, that such largest values give rise to the universal fidelity that is independent of the system size.
Keywords: estimation of entanglement, Werner-type N-qudit states, quantum Fisher information
Acknowledgements. This work was supported in part by the grants from the National Natural Science Foundation of China (project no. 11775084) and the grant-in-aid for scientific research from the Japan Society for the Promotion of Science (projects nos. 26400391 and 16K05484) and performed according to the Russian Government Program of Competitive Growth of Kazan Federal University.
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Recieved
November 24, 2017
Abe Sumiyoshi, Professor of Physics Division; Professor of Department of Physical Engineering; Leading Researcher of Institute of Physics
College of Information Science and Engineering, Huaqiao University
Xiamen Campus: No. 668 Jimei Avenue, Xiamen, Fujian, 361021 China
Mie University
1577 Kurimamachiya-cho, Tsu, Mie, 514-8507 Japan
Kazan Federal University
ul. Kremlevskaya 18, Kazan, 420008 Russia
E-mail: suabe@sf6.so-net.ne.jp
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