Schedule May 25, 2012
Lower Bounds on the Scrambling Time
Nima Lashkari (McGill Univ.)

Authors: Nima Lashkari, Douglas Stanford, Matthew Hastings, Tobias Osborne, Patrick Hayden

Scrambling is a strong form of thermalization applicable to closed system evolution. We define the scrambling time to be the minimum time for the information about the initial states to be spread out among degrees of freedom such that it can only be recovered by measuring subsystems of order one. We explore the connection between scrambling and signaling. Using the Lieb-Robinson techniques and controlled mean-field approximations we find logarithmic lower bounds on the scrambling time of systems with finite norm terms in the Hamiltonian. The bounds hold in spite of any non-local structure in the Hamiltonian, which might permit every degree of freedom to interact directly with every other one.

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