Estimating entanglement in a class of N-qudit states

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

E-mail: suabe@sf6.so-net.ne.jp

Received November 24, 2017

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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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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.

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