The problem with the geometric discord

Abstract

We argue that the geometric discord introduced in [B. Dakic, V. Vedral, and C. 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/non-classicality 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.

5 pages. Changes in ver 2: typos corrected, added short proof of monotonicity of standard quantum discord under one-side action. This note is meant to stimulate discussion in the community: comments are welcome