  Information in a chaotic quantum system will scramble across the system,
preventing any local measurement from reconstructing it. The scrambling
dynamics is key to understanding a wide range of quantum many-body systems.
Here we use Holevo information to quantify the scrambling dynamics, which shows
a phase-transition-like behavior. When applying long random Clifford circuits
to a large system, no information can be recovered from a subsystem of less
than half the system size. When exceeding half the system size, the amount of
stored information grows by two bits of classical information per qubit until
saturation through another sharp unanalytical change. We also study critical
behavior near the transition points. Finally, we use coherent information to
quantify the scrambling of quantum information in the system, which shows
similar phase-transition-like behavior.
