Recently, the resource theory of imaginarity has attracted much attention. As with other resources such as quantum correlations, coherence, and asymmetry, an important task in the resource theory of imaginarity is deimaginarity, which is to transform a state into a free state in the resource theory of imaginarity by the random covariant-free unitary operations. Here, we consider an asymptotic limit of infinitely many copies and vanishingly small error, and analyze the deimaginarity cost. We prove that the deimaginarity cost of a state is equal to its regularized relative entropy of imaginarity, which can be seen as an operational interpretation of the relative entropy of imaginarity.

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• Quantum correlations, foundations & formalism
• Resource theories