Lower bounds on the quantum Fisher information based on the variance and various types of entropies

Lower bounds on the quantum Fisher information based on the variance and various types of entropies

Seminar author:Geza Toth

Event date and time:01/10/2018 12:00:pm

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We examine important properties of the difference between the variance
and the quantum Fisher information over four, i.e., (ΔA)2−FQ[ϱ,A]/4.
We find that it is equal to a generalized variance defined in Petz [J.
Phys. A 35, 929 (2002)] and Gibilisco, Hiai, and Petz [IEEE Trans.
Inf. Theory 55, 439 (2009)]. We present an upper bound on this
quantity that is proportional to the linear entropy. As expected, our
relations show that for states that are close to being pure, the
quantum Fisher information over four is close to the variance. We also
obtain the variance and the quantum Fisher averaged over all Hermitian
operators, and examine their relation to the von Neumann entropy.

[1] G. Toth, arxiv:1701.07461.