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arXiv · 2407.11755

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

Chellasamy Jebarathinam·Debarshi Das·Huan-Yu Ku·Debasis Sarkar·Hsi-Sheng Goan
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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.

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Chellasamy Jebarathinam, Debarshi Das, Huan-Yu Ku, Debasis Sarkar, Hsi-Sheng Goan. 2024-07-16. Operational simultaneous correlations in complementary bases of bipartite states via one-sided semi-device-independent steering. https://doi.org/10.1103/physreva.111.062403

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