Problem with geometric discord

We argue that the geometric discord introduced by Dakic, Vedral, and Brukner [Phys. Rev. Lett. 105, 190502 (2010)] is not a good measure for the quantumness of correlations, as it can increase even under trivial local reversible operations of the party whose classicality or nonclassicality is not tested. On the other hand it is known that the standard, mutual-information-based discord does not suffer this problem; a simplified proof of such a fact is given.