Dominance of quantum over classical correlations: entropic and geometric approach

Recently, it has been shown that there exist quantum states for which quantum correlations dominate over classical correlations. Inspired by this observation, we investigate the problem of quantum correlations dominance for two-qubit Bell diagonal states in the Ollivier--Zurek paradigm, using both entropic and geometric approach to quantification of classical and quantum correlations. In particular, we estimate numerically the amount of two-qubit Bell diagonal states for which quantum correlations dominate over classical correlations, and vice versa. Moreover, we show that in general these two approaches to quantification of correlations provide ambiguous results.