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

TL;DR

This paper investigates how simultaneous correlations in complementary bases relate quantitatively to quantum steering in two-qubit Bell-diagonal states, revealing that higher correlations imply stronger steering.

Contribution

It establishes a quantitative relationship between correlations in mutually unbiased bases and quantum steering for Bell-diagonal states, highlighting the resource role of these correlations.

Findings

Higher simultaneous correlations in complementary bases correlate with increased quantum steering.

The relation holds for both two and three setting steering scenarios.

The study provides a quantitative framework linking correlations and steering in 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.