Akram Touil and Sebastian Deffner
A thermodynamic description of quantum scrambling for open quantum system dynamics is formulated, leading to universal applications that range from black holes to ion trap systems.
PRX Quantum 2, 010306 – Published 13 January 2021
In a recent paper, the authors have shown that scrambling in isolated quantum systems can be quantified by mutual information. In this new study, they further extend the analysis to open quantum systems. In particular, they show that the mutual information can be separated into unique contributions arising from either scrambling or decoherence. This separation of terms lends itself naturally to the further derivation of statements of the second law of thermodynamics for scrambling of information in open systems. The general findings are then illustrated for a variety of models, including the Sachdev-Ye-Kitaev, the Maldacena-Qi, the XXX, the mixed-field Ising, and the Lipkin-Meshkov-Glick model with decoherence in energy or in the computational basis.
This work may have universal applications, from black holes (as their intense gravitational field is a decoherence channel) to ion-trap systems, for which information scrambling has been observed experimentally.