  Quantum information is scrambled via a chaotic time evolution in many-body
systems. Clarifying how and to what extent we can recover the quantum
information from the scrambled state is a central issue of today's physics,
since it commonly appears as an essential factor in various topics including
irreversibility of quantum chaotic dynamics, fault-tolerant quantum
computation, and black hole information paradox. In realistic settings,
symmetry can ubiquitously exist in scrambling dynamics. Here we establish
fundamental limitations on the information recovery arising from the Lie group
symmetries in the scrambling dynamics. The results are applicable to many
situations, including the Hayden-Preskill black hole model with symmetry where
the success rate of the information recovery qualitatively changes from the
original no-symmetry case. Our findings show a close relationship between
information recovery, symmetry, and quantum coherence, and that symmetry
hinders the quantum information recovery.
