CM In the literature: open

Measured Lyapunov exponent versus temperature in a quantum simulator

In plain words

OTOC experiments so far probe effectively infinite-temperature states, where quantum limits on chaos do not show. Measuring the scrambling rate in a cold many-body state would test the chaos bound directly.

Precise statement

In a quantum simulator realizing a nonintegrable lattice model (e.g. 2D Bose-Hubbard at $U/J \sim 10$ or a Rydberg array), measure the regularized thermal OTOC growth rate $\lambda_{L}(T)$ for $k_{B}T$ below the bandwidth using a time-reversal protocol. Answer: $\lambda_{L}(T)$ with error bars over a factor of 5 in T, compared with $2\pi k_{B}T/\hbar$.

What would settle it

An experiment preparing thermal states at several temperatures and extracting an exponential OTOC growth window at each.

Status in the literature

OTOC experiments to date (trapped ions, superconducting processors) probe effectively infinite-temperature or circuit states.