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Chinese Physics Letters

Concurrence and Wigner–Yanase Skew Information

Li Tang, Zeqian Chen

Published Feb 24, 2006• 7 citations
Publisher

Abstract

A measure of entanglement on n qubits is defined in terms of Wigner–Yanase skew information. It is shown that the measure coincides essentially with the concurrence on two qubits. This uncovers the information-theoretic meaning of the concurrence of entangled states.
DOI
10.1088/0256-307x/23/3/005

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The Wigner-Araki-Yanase theorem puts a limitation on the measurement of observables in the presence of a conserved quantity, and the notion of Wigner-Yanase skew information quantifies the amount of information on the values of observables not commuting with the conserved quantity. We demonstrate that the statistical idea underlying the skew information is the Fisher information in the theory of statistical estimation. A quantum Cramér-Rao inequality and a new uncertainty relation in terms of the skew information are established, which shed considerable new light on the relationships between quantum measurement and statistical inference. The result is applied to estimating the evolution speed of quantum states.