Witnessing quantum scrambling with steering

Quantum information scrambling describes the delocalization of local information to global information in the form of entanglement throughout all possible degrees of freedom. A well-known scrambling witness is the so-called out-of-time-ordered correlator (OTOC), which can identify scrambling because it is closely related to the incompatibility of two separate operators at two different times. In this work, we show that quantum scrambling can also be witnessed by using techniques from temporal quantum steering. We can do so because, for qubits systems, there is a fundamental equivalence between the Choi-Jamiolkowski isomorphism and the pseudo-density matrix formalism used in temporal quantum correlations. Based on this relationship, we propose a scrambling witness, based on a measure of temporal steering called the robustness. We justify the properties of this quantity as a witness of scrambling by proving that the quantity vanishes when the channel is non-scrambling.