On Scrambling Times of Quantum Systems, Including Black Holes
Talkat Near-Term Quantum Computers: Fault Tolerance + Benchmarking + Quantum Advantage + Quantum Algorithms · 2024-04-22..04-26·
summary
Argues that the commonly used OTOC scrambling time (outsizedly short) and the time to become nearly maximally entangled are distinct: a Clifford-on-a-binary-tree toy model shows OTOC equilibration in linear radius time while entanglement scrambling scales like 2^n, exponentially longer. Applies this to black holes using photon-sphere cell counting and Hawking-radiation bandwidth, rederiving Hayden–Preskill’s M log M lower bound and concluding strong scrambling must be at least order M^2 unless one accepts radical nonstandard physics.
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chapters (9)
- 0:00Scrambling times and black holes
- 1:03Black holes and information paradox
- 14:15Scrambling time in quantum systems
- 21:59Toy model for scrambling times
- 29:32Fast scrambling conjecture
- 33:33Hawking radiation transfer
- 40:51Lower bound for scrambling time
- 41:38Black hole microstates
- 44:44Summary and open questions
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