Comparison of different measures for quantum discord under non-Markovian noise

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.