Ancilla-free measurement of out-of-time-ordered correlation functions: General measurement protocol and Rydberg atom implementation

We introduce a protocol that gives access to out-of-time-ordered correlation functions in many-body quantum systems. Unlike other such protocols, our proposal, which can be applied to arbitrary initial states, neither requires ancilla degrees of freedom to the quantum system of interest, nor has the need for randomized measurements. Nontrivial experimental capabilities required to implement the protocol are single-site measurements, single-site rotations, and backwards time evolution. To exemplify the implementation of the protocol, we put forward a strategy for Hamiltonian sign inversion $H\to-H$ in arrays of Rydberg-dressed atoms. In this way, a complete and practical toolbox is obtained for the measurement of out-of-time-ordered correlations in equilibrium and nonequilibrium situations.