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