Sharpening complex quantum dynamics with teleportation protocols (and gravity)

The richness of complex quantum dynamics has invited the use of a plethora of classical terms with no agreed-upon quantum meanings, such as ergodicity, scrambling, and chaos, to describe them. We will describe recent progress in assigning a precise operational meaning to some foundational "indicators" of complex dynamics, traditionally associated with randomness, in terms of the ability of quantum systems to perform specific tasks. In our case, these tasks take the form of gravity-inspired quantum teleportation protocols tied to different forms of orthonormality. Our primary example concerns random-matrix-like energy level statistics, often considered a "defining" feature of "quantum chaos". We show that this feature can be directly used as a resource for teleportation through its ability to generate orthonormal states via "ergodic" dynamics, which has a gravitational parallel in the nonperturbative quantum dynamics of wormholes. Another example is a two-way teleportation protocol that probes operator entanglement in space and time, which extends protocols for one-way information recovery from toy models of black holes associated with the "scrambling" dynamics of random operators.