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Wednesday, November 13th 2019

1:25 pm:

Scrambling of quantum information is the process by which information initially stored in the local degrees of freedom of a quantum many-body system spreads over its many-body degrees of freedom, becoming inaccessible to local probes and thus apparently lost. Scrambling and entanglement are considered key concepts that reconcile seemingly unrelated behaviors including thermalization of isolated quantum systems and information loss in black holes. Moreover, these two concepts have revolutionized our understanding of non-equilibrium phenomena. In this talk I will argue that a specific family of fidelity out-of-time-order correlators (FOTOCs), recently measured in a trapped-ion quantum simulator via time reversal of the many-body dynamics followed by a fidelity measurement can serve as a unifying diagnostic tool that elucidates the intrinsic connection between fast scrambling, volume law entanglement, ergodicity, quantum chaos, and the butterfly effect in the associated semiclassical dynamics of the system. I will illustrate the utility of FOTOCs by presenting our calculations in the Dicke model an iconic model in quantum optics, recently implemented in atomic and trapped-ion setups. This model describes the coupling of a large spin to an oscillator and features rich behaviors, including a quantum phase transition and chaos. I will show that FOTOCs provide a direct measure of the Renyi entropy and thus give us access to study quantum thermalization. These findings open a path for the experimental use of FOTOCs to quantify fast scrambling, to determine bounds on quantum information processing and to identify possible candidates of black hole analogs in controllable quantum systems.

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