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Studying the behavior of quantum information scrambling in various quantum systems is an active area of research. Recently, Sharma et al. K.K. Sharma, V.P Gerdt, Quantum Inf. Process 20, 195 (2021) have shown the mathematical connection between quantum information scrambling (QIS) and bipartite entanglement in non-thermal states. In the present work, we elegantly generalize this mathematical connection and study such connections in X-states, non-maximally entangled Bell states, and Werner states
Sharma et al. (Fri,) studied this question.