Most experimental protocols for measuring scrambling require time evolution with a Hamiltonian and with the Hamiltonian's negative counterpart (backward time evolution). Engineering controllable quantum many-body systems for which such forward and backward evolution is possible is a significant experimental challenge. Furthermore, if the system of interest is quantum chaotic, one might worry that any small errors in the time reversal will be rapidly amplified, obscuring the physics of scrambling. This paper undermines this expectation: We exhibit a renormalization protocol that extracts nearly ideal out-of-time-ordered-correlator measurements from imperfect experimental measurements. We analytically and numerically demonstrate the protocol's effectiveness, up to the scrambling time, in a variety of models and for sizable imperfections. The scheme extends to errors from decoherence by an environment.

• Received 11 February 2018
• Revised 8 May 2018

DOI:https://doi.org/10.1103/PhysRevA.97.062113