Entanglement in $$ \mathrm{T}\overline{\mathrm{T}} $$ and root-$$ \mathrm{T}\overline{\mathrm{T}} $$ deformed AdS3/CFT2

A bstract In this work, we investigate the effects of $$ \mathrm{T}\overline{\mathrm{T}} $$ T T ¯ and root- $$ \mathrm{T}\overline{\mathrm{T}} $$ T 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 and marginal deformations and quantum information-theoretic quantities, shedding light on the entanglement structure of deformed theories.