Optimal generalized variance and quantum Fisher information

Details Optimal generalized variance and quantum Fisher information Optimal generalized variance and quantum Fisher information

2011-09-13

arxiv.org/abs/1109.2831v1

Physics

Quantum Physics

17 pages, no figures, LaTeX

Scientific paper

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)].

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