Remedying the local ancilla problem with geometric discord

The geometric discord, as introduced by Dakic, Vedral, and Brukner [Phys. Rev. Lett. 105, 190502 (2010)], is a significant figure of merit for quantum correlations with wide applications. However, it has a curious drawback in that it may change reversibly by trivially adding a local ancilla, as recently criticized by Piani [Phys. Rev. A 86, 034101 (2012)]. This casts doubt on the information content and usage of geometric discord. In this work, we show that this problem with geometric discord can be remedied simply by starting from the square root of a density operator, rather than the density operator itself, in defining the discord. Moreover, most other basic properties and analytical aspects of the original geometric discord can be carried over to this modified discord. Due to the square-root character, which is reminiscent of probability amplitudes ubiquitous in quantum theory, the modified discord seems to capture quantum correlations in a more intrinsic and informational fashion.