Revealing the quantitative relation between simultaneous correlations in complementary bases and quantum steering for two-qubit Bell diagonal states

Abstract: The present work is motivated by the question as to what aspect of correlation entailed by the two-qubit state serves as the appropriate quantitative resource for steering. To this end, considering Bell-diagonal states, suitable measures of simultaneous correlations in two and three complementary (mutually unbiased) bases are identified as the relevant resources for quantum steering. Quantitative relations between appropriate measures of quantum steering and the corresponding measures of simultaneous correlations in complementary bases are demonstrated which ensure that for two qubit steerable Bell-diagonal states, higher value of simultaneous correlations in mutually unbiased bases necessarily implies higher degree of quantum steering, both for two and three setting steering scenarios.