Statement
Problem 4.1 of Goto et al.: the Hayden–Preskill protocol models a black hole as a Haar-random unitary and radiation as its output, giving a clean account of information recovery. How can it be refined to include realistic features — energy conservation, geometric locality, finite temperature, actual evaporation dynamics?
Why It Matters
Peripheral to the group (this is holographic QEC / scrambling, not the group’s flat-space QI). It is the toy-model backdrop to the Page curve material in the CFT course.
What We Know
- Hayden–Preskill: after the Page time, information thrown into a black hole is recoverable from the radiation given the early radiation.
- Haar-randomness is an idealization; real dynamics are local, energy-conserving Hamiltonians.
Possible Approaches
- Replace Haar unitaries with structured (energy-conserving, local) ensembles — see many-body-dynamics-for-near-haar-encoding.
- Embed the protocol in an evaporating-black-hole / island computation.