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Entanglement in $\text{T}\bar{\text{T}}$ and root-$\text{T}\bar{\text{T}}$ deformed AdS$_3$/CFT$_2$

In this work, we investigate the effects of $\text{T}\bar{\text{T}}$ and root-$\text{T}\bar{\text{T}}$ deformations on reflected and entanglement entropy in the context of both pure and mixed state entanglement measures. Utilizing a mixed boundary condition framework, we analyze how these deformations modify entanglement structures and explore their implications in three-dimensional AdS space. Our results provide insights into the interplay between solvable irrelevant deformations and quantum information-theoretic quantities, shedding light on the entanglement structure of deformed theories.