Probing quantum dynamics using out-of-time-ordered measurements

Recently, out of time-ordered correlators (OTOCs), i.e., correlators of the form 〈W(t)V(0)W(t)V(0)〉 where W and V are local operators, have been used extensively to study quantum dynamics in various quantum statistical phases, such as chaotic, many-body-localized and delocalized integrable systems. These measures capture subtle quantum correlations that are missed by ordinary time-ordered or retarded correlators. However, measuring OTOCs experimentally requires creating two identical copies of the system, applying the out-of-time-ordered operator on one of them, and taking the overlap of the resultant state with the second copy. This procedure becomes prohibitively difficult for any reasonably large system. In this work, we propose an alternate quantity that we dub the out-of-time-ordered measurement (OTOM) for probing quantum dynamics. The OTOM is closely related to the OTOC and hence, inherits many of its properties. However, it can be measured experimentally with a single copy of the system. Thus, it overcomes the experimental challenge of scalability that the OTOC faces, and makes it possible to study correlations in quantum dynamics that are out of reach experimentally using OTOCs.