Probing out-of-time-order correlators using thermofield double states

We propose a new family of protocols for measurements of out-of-time order correlators (OTOCs) that do not require backward time evolution. Instead, they rely on ordinary time-ordered measurements performed in the thermofield double (TFD) state, an entangled state formed between two identical copies of a quantum system. In particular, we show how Lyapunov exponents of quantum chaotic systems can be extracted from various time-ordered correlators (including equilibrium Green’s functions) in the TFD state. Importantly, TFD states can be realized as ground states of simple Hamiltonians coupling two identical systems, which underlies their usefulness for experimental explorations of quantum chaos. We numerically test our protocols on two coupled SYK models, recently proposed to be dual to an eternal traversable wormhole, and discuss possible realizations of this setup.