Abstract
When
quantum information "scrambles", 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 antithetical 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. I will show 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 associated butterfly effect in the semiclassical dynamics
of the system. I will demonstrate the utility of the FOTOCs using the
Dicke model which has been recently benchmarked in a 2d trapped-ion
quantum simulator.