Hannover 2013 – scientific programme

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Q: Fachverband Quantenoptik und Photonik

Q 13: Quantum information: Concepts and methods I

Q 13.4: Talk

Monday, March 18, 2013, 14:45–15:00, E 214

Extremal properties of the variance and the quantum Fisher information — •Géza Tóth^1,2,3 and Dénes Petz⁴ — ¹Theoretical Physics, University of the Basque Country UPV/EHU, E-48080 Bilbao, Spain — ²IKERBASQUE, Basque Foundation for Science, E-48011 Bilbao, Spain — ³Wigner Research Centre for Physics, H-1525 Budapest, Hungary — ⁴Alfréd Rényi Institute of Mathematics, Reáltanoda utca 13-15, H-1051 Budapest, Hungary

We show that the variance is its own concave roof. For rank-2 density matrices and operators with zero diagonal elements in the eigenbasis of the density matrix, we show analytically that the quantum Fisher information is 4 times the convex roof of the variance. Strong numerical evidence suggests that the quantum Fisher information is very close to the convex roof even for operators with nonzero diagonal elements or density matrices with a rank larger than 2. Hence, we conjecture that the quantum Fisher information is 4 times the convex roof of the variance even for the general case.