Operational simultaneous correlations in complementary bases of bipartite states via one-sided semi-device-independent steering

TL;DR

This paper links one-sided semi-device-independent quantum steering to operational measures of simultaneous correlations in mutually unbiased bases, providing new insights and classifications for bipartite quantum states with geometric visualization.

Contribution

It establishes a novel operational interpretation of simultaneous correlations via one-sided semi-device-independent steering and classifies two-qubit states based on these correlations.

Findings

Operational identification of simultaneous correlations as steering.

Quantification of correlations in Bell-diagonal states.

Geometric visualization using quantum steering ellipsoid.

Abstract

Recently, a different form of quantum steering, i.e., certification of quantum steering in a one-sided semi-device-independent way, has been formulated [Jebarathinam \etal Phys. Rev. A 108, 042211 (2023)]. In this work, we use this phenomenon to provide operational simultaneous correlations in mutually unbiased bases as quantified by the measures in [Wu \etal Scientific Reports 4, 4036 (2014)]. First, we show that for any bipartite state, such measure of simultaneous correlations in two mutually unbiased bases can be operationally identified as exhibiting one-sided semi-device-independent steering in a two-setting scenario. Next, we demonstrate that for two-qubit Bell-diagonal states, quantifying one-sided semi-device-independent steerability provides an operational quantification of information-theoretic quantification of simultaneous correlations in mutually unbiased bases. Then, we provide a different classification of two-qubit separable states with the above-mentioned information-theoretic quantification of simultaneous correlations in mutually unbiased bases and the quantification of one-sided semi-device-independent steerability. Finally, we invoke quantum steering ellipsoid formalism to shed intuitions on the operational characterization of simultaneous correlations in complementary bases of two-qubit states via one-sided semi-device-independent steerability. This provides us with a geometric visualization of the results.