Quantum scrambling and the growth of mutual information

Abstract

Understanding what happens to a qubit thrown into a black hole is not an easy task; is the information lost to any outside observer or can it be retrieved by local measurements? This problem boils down to studying the scrambling of information over the event horizon, which draws attention to a general class of problems: scrambling of quantum information. In our work, we study the scrambling properties of quantum systems through the mutual information (MI). To this end, we lower bound the MI by the Out-of- Time-Order Correlators (OTOC) and determine its dynamical properties, relating the MI to thermodynamic quantities such as irreversible entropy production. We then illustrate, through examples, the thermodynamic significance of the MI for quantum information scrambling. Thus, as a main result, we establish a clear link between the MI and the OTOC, which enables us to probe the thermodynamics of quantum information scrambling and opens the door for further studies of the thermodynamics of quantum chaotic systems.