Stuttgart 2012 – scientific programme

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Q: Fachverband Quantenoptik und Photonik

Q 31: Quanteninformation: Konzepte und Methoden 4

Q 31.1: Talk

Tuesday, March 13, 2012, 14:00–14:15, V7.01

Optimal generalized variance and quantum Fisher information — •Géza Tóth^2,3,4 and Dénes Petz¹ — ¹Theoretical Physics, The University of the Basque Country, E-48080 Bilbao, Spain — ²IKERBASQUE, Basque Foundation for Science, E-48011 Bilbao, Spain — ³Research Institute for Solid State Physics and Optics, H-1525 Budapest, Hungary — ⁴Alfréd Rényi Institute of Mathematics, Reáltanoda utca 13-15, H-1051 Budapest, Hungary

We define the generalized variance based on requiring that (i) it equals the usual variance for pure states and (ii) it is concave. For a quantum system of any size, we show that the usual variance is the smallest generalized variance, which makes it optimal for using it in entanglement criteria based on uncertainty relations. Similarly, we define the generalized quantum Fisher information, replacing the requirement of concavity by convexity. For rank-2 density matrices, we show that the quantum Fisher information is the largest among generalized quantum Fisher informations. We relate our findings to the results of [D. Petz, J. Phys. A: Math. Gen. 35, 79 (2003); P. Gibilisco, F. Hiai and D. Petz, IEEE Trans. Inform. Theory 55, 439 (2009)].