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There has been recent progress in understanding chaotic features in many-bodyquantum systems. Motivated by the scrambling of information in black holes, ithas been suggested that the time dependence of out-of-time-ordered (OTO)correlation functions such as $\langle O_2(t) O_1(0) O_2(t) O_1(0) \rangle $ isa faithful measure of quantum chaos. Experimentally, these correlators arechallenging to access since they apparently require access to both forward andbackward time evolution with the system Hamiltonian. Here, we propose aprotocol to measure such OTO correlators using an ancilla which controls thedirection of time. Specifically, by coupling the state of ancilla to the systemHamiltonian of interest, we can emulate the forward and backward timepropagation, where the ancilla plays the role of a 'quantum clock'. Within thisscheme, the continuous evolution of the entire system (the system of interestand the ancilla) is governed by a time-independent Hamiltonian. Our protocol isimmune to errors that could occur when the direction of time evolution isexternally controlled by a classical switch.

Measurement of many-body chaos using a quantum clock