Direct approach to quantum extensions of Fisher information |
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Authors: | Ping Chen Shunlong Luo |
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Institution: | (1) Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100080, China |
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Abstract: | By manipulating classical Fisher information and employing various derivatives of density operators, and using entirely intuitive
and direct methods, we introduce two families of quantum extensions of Fisher information that include those defined via the
symmetric logarithmic derivative, via the right logarithmic derivative, via the Bogoliubov-Kubo-Mori derivative, as well as
via the derivative in terms of commutators, as special cases. Some fundamental properties of these quantum extensions of Fisher
information are investigated, a multi-parameter quantum Cramér-Rao inequality is established, and applications to characterizing
quantum uncertainty are illustrated.
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Keywords: | Fisher information density operators logarithmic derivatives commutator quantum Fisher information |
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