  The Hayden-Preskill protocol is a qubit-toy model of the black hole
information paradox. Based on the assumption of scrambling, it was revealed
that quantum information is instantly leaked out from the quantum many-body
system that models a black hole. In this paper, we extend the protocol to the
case where the system has symmetry and investigate how the symmetry affects the
leakage of information. We especially focus on the conservation of the number
of up-spins. Developing a partial decoupling approach, we first show that the
symmetry induces a delay of leakage and an information remnant. We then clarify
the physics behind them: the delay is characterized by thermodynamic properties
of the system associated with the symmetry, and the information remnant is
closely related to the symmetry-breaking of the initial state. These relations
bridge the information leakage problem to macroscopic physics of quantum
many-body systems and allow us to investigate the information leakage only in
terms of physical properties of the system.
