Complementarity Reveals Entanglement Sharing in Sequential Quantum Measurements

Abstract: We investigate entanglement sharing in a two-qubit sequential measurement scenario using three complementary classical correlation metrics: mutual information (I), 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 trade-off between measurement disturbance and complementary correlation recovery, which is essential for quantum resource reuse problems.