We provide analytical expressions for classical and total trace-norm (Schatten 1-norm) geometric correlations in the case of two-qubit $X$ states. As an application, we consider the open-system dynamical behavior of such correlations under phase and generalized amplitude damping evolutions. Then, we show that geometric classical correlations can characterize the emergence of the pointer basis of an apparatus subject to decoherence in either Markovian or non-Markovian regimes. In particular, as a non-Markovian effect, we obtain a time delay for the information to be retrieved from the apparatus by a classical observer. Moreover, we show that the set of initial $X$ states exhibiting sudden transitions in the geometric classical correlation has nonzero measure.

• Received 30 April 2015

DOI:https://doi.org/10.1103/PhysRevA.92.032307