  Two geometric measures for quantum discord were recently proposed by Modi et
al. [Phys. Rev. Lett. 104, 080501 (2010)] and Dakic et al. [Phys. Rev. Lett.
105, 190502 (2010)]. We study the similarities and differences for total
quantum correlations of Bell-diagonal states using these two geometry-based
quantum discord and the original quantum discord. We show that, under
non-Markovian dephasing channels, quantum discord and one of the geometric
measures stay constant for a finite amount of time, but not the other geometric
measure. However, all the three measures share a common sudden change point.
Our study on critical point of sudden transition might be useful for keeping
long time total quantum correlations under decoherence.
