Distinguishing Information Scrambling from Decoherence in a Trapped Ion Quantum Simulator

The dynamics of a strongly interacting many-body system causes the scrambling of quantum information, wherein local information becomes ``hidden'' in non-local observables. Recently, a powerful theoretical proxy to diagnose scrambling has emerged in the form of out-of-time-ordered correlation functions (OTOCs). However, the direct and unambiguous experimental measurement of scrambling via such OTOCs remains an essential challenge. This challenge can be summarized as follows: for a generic interacting system, the scrambling of quantum information will cause OTOCs to decay to zero. However, both decoherence and imperfect experimental controls (e.g.~time reversal) will \emph{also} cause OTOCs to decay to zero. Inspired by the Hayden-Preskill variant of the black hole information problem, we describe a quantum-teleportation-based scheme which explicitly detects both the ``erroneous decay'' of OTOCs (from noise and decoherence) as well as the desired decay due to information scram bling. We present the experimental realization of this scheme on a 7-qubit trapped ion quantum computer. The scrambling operation is realized via a digital 3-qubit quantum gate, and teleportation fidelities of up to ~80\% are achieved enabling us to bound the true scrambling induced decay of the OTOC.