Coherence extraction from measurement-induced disturbance

We establish an operational connection between coherence and quantum correlation by showing that, Alice can create quantum coherence on Bob's side using local selective measurement as long as the previously shared bipartite state has non-vanishing quantum correlation on $B$, and the maximum average coherence she can extract can not surpass the $B$-side quantum correlation in the initial bipartite state. Steering-induced coherence is introduced to characterize Alice's ability to extract quantum coherence on Bob's side. For pure states and the maximally correlated states, the steering-induced relative entropy of coherence is proved to reach the initially shared quantum correlation which is measured by the relative entropy of $B$-side measurement-induced disturbance. The condition to reach the upper bound of quantum correlation varies for different measures of coherence. While the steering-induced $l_1$-norm of coherence is shown reach the initially shared quantum correlation (measured by trace-norm of $B$-side measurement-induced disturbance) for any two-qubit states, an example is found whose steering-induced relative entropy of coherence is strictly less than the relative entropy of $B$-side measurement-induced disturbance.

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