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    Entanglement sharing in sequential quantum measurements revealed by complementarity

    Zinuo Cai and Changliang Ren*

    • Key Laboratory of Low-Dimension Quantum Structures and Quantum Control of Ministry of Education, Synergetic Innovation Center for Quantum Effects and Applications, Xiangjiang-Laboratory and Department of Physics, Hunan Normal University, Changsha 410081, China; Hunan Research Center of the Basic Discipline for Quantum Effects and Quantum Technologies, Hunan Normal University, Changsha 410081, China; and Institute of Interdisciplinary Studies, Hunan Normal University, Changsha 410081, China

    • *Contact author: renchangliang@hunnu.edu.cn

    Phys. Rev. A 113, 012217 – Published 14 January, 2026

    DOI: https://doi.org/10.1103/m1gb-s1fj

    Abstract

    We investigate entanglement sharing in a two-qubit sequential measurement scenario using three complementary classical correlation metrics: mutual information (I), a sum of conditional probabilities (S), and the Pearson correlation coefficient (C). By investigating both weak measurement and probabilistic projective measurement (PPM) strategies in unilateral and bilateral scenarios, the phenomenon of entanglement sharing is conclusively certified when multiple pairs of classical correlation metrics simultaneously exceed their thresholds. Our investigation reveals that weak measurement strategies are more favorable than PPM for exhibiting entanglement sharing, regardless of the scenario. Furthermore, the mutual information criterion fails to characterize entanglement sharing in the bilateral scenario, while the Pearson correlation criterion (C) is proven to be the most robust across all strategies and scenarios. These findings unveil a critical tradeoff between measurement disturbance and complementary correlation recovery, which is essential for quantum resource reuse problems.

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