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

• URL: http://arxiv.org/abs/2407.11755v3
• Date: Fri, 07 Feb 2025 02:03:51 GMT
• Title: Operational simultaneous correlations in complementary bases of bipartite states via one-sided semi-device-independent steering
• Authors: Chellasamy Jebarathinam, Debarshi Das, Huan-Yu Ku, Debasis Sarkar, Hsi-Sheng Goan,
• Abstract summary: 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. 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. 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.
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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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