# Erlangen 2018 – wissenschaftliches Programm

## Bereiche | Tage | Auswahl | Suche | Aktualisierungen | Downloads | Hilfe

# Q: Fachverband Quantenoptik und Photonik

## Q 15: Quantum Information (Concepts and Methods) II

### Q 15.3: Vortrag

### Montag, 5. März 2018, 14:45–15:00, K 1.019

**Lower bounds on the quantum Fisher information based on the variance and various types of entropies** — •Géza Tóth — Theoretical Physics, University of the Basque Country UPV/EHU, E-48080 Bilbao, Spain — Wigner Research Centre for Physics, H-1525 Budapest, Hungary — IKERBASQUE, Basque Foundation for Science, E-48011 Bilbao, Spain

We examine important properties of the difference between the variance and the quantum Fisher information over four, i.e., var(A)-F_Q[rho,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.