Proposal to measure out-of-time-ordered correlations using Bell states

Abstract

We present a protocol to experimentally measure the infinite-temperature out-of-time-ordered correlation (OTOC) -- which is a probe of quantum information scrambling in a system -- for systems with a Hamiltonian which has either a chiral symmetry or a particle-hole symmetry. We show that the OTOC can be obtained by preparing two entangled systems, evolving them with the Hamiltonian, and measuring appropriate local observables. At the cost of requiring two copies of the system and putting restrictions on the Hamiltonian's symmetries, we show that our method provides some advantages over existing methods -- it can be implemented without reversing the sign of the Hamiltonian, it requires fewer measurements than schemes based on implementing the SWAP operator, and it is robust to imperfections like some earlier methods. Our ideas can be implemented in currently available quantum platforms.