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Information scrambling, which is the spread of local information through asystem's many-body degrees of freedom, is an intrinsic feature of many-bodydynamics. In quantum systems, the out-of-time-ordered correlator (OTOC)quantifies information scrambling. Motivated by experiments that have measuredthe OTOC at infinite temperature and a theory proposal to measure the OTOC atfinite temperature using the thermofield double state, we describe a protocolto measure the OTOC in a finite temperature spin chain that is realizedapproximately as one half of the ground state of two moderately-sized coupledspin chains. We consider a spin Hamiltonian with particle-hole symmetry, forwhich we show that the OTOC can be measured without needing sign-reversal ofthe Hamiltonian. We describe a protocol to mitigate errors in the estimatedOTOC, arising from the finite approximation of the system to the thermofielddouble state. We show that our protocol is also robust to main sources ofdecoherence in experiments.

Proposal for measuring out-of-time-ordered correlators at finite temperature with coupled spin chains