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Towards the fast scrambling conjecture


The theory of quantum error correction has focused attention on the relationship between the relaxation timescales of black holes and their information retention time. Motivated by the consistency of black hole complementarity, Sekino and Susskind have conjectured that no physical system can delocalize, or "scramble", its internal degrees of freedom in time faster than (1/T) log S, where T is temperature and S the system's entropy. By considering a number of toy examples and general Lieb-Robinson-type causality bounds, I'll explore the range of validity of the conjecture. Specific toy examples suggest that logarithmic-time information scrambling is indeed possible, while the adaptation of causality arguments to nonlocal Hamiltonians excludes faster scrambling under quite general hypotheses. (Joint work with Nima Lashkari, Douglas Stanford, Matthew Hastings and Tobias Osborne.)