Fisher information and Stam inequality on a finite group ( Bull . London . Math . Soc . 40 (2008) 855–862)
Abstract
Bull. London Math. Soc. 42 (2010) 973 e 2010 London Mathematical Society doi:10.1112/blms/bdq067 Editorial statement Fisher information and Stam inequality on a finite group (Bull. London Math. Soc. 40 (2008) 855862) The editors thank the authors of the paper [2] for pointing out an error in the paper. The Stam inequality 1 IX+Y 1 1 + , IX IY is known to hold on finite cyclic groups and on the circle. The proof uses a conditional expectation property of the Fisher score. Lemma 3.1 in [2], extending this to finite groups, is not correct as stated, and the claimed Stam-like inequality does not hold for finite non-abelian groups. A detailed discussion and counterexamples may be found in [1].