Thermodynamics of quantum information scrambling

TL;DR

A method for the measurement of OTOCs based on the so-called two-point measurement scheme developed in the field of nonequilibrium quantum thermodynamics is reported on, which provides a clear-cut interpretation of quantum information scrambling in terms ofNonequilibrium fluctuations of thermodynamic quantities, such as work and heat.

Abstract

Scrambling of quantum information can be conveniently quantified by so called out-of-time-order-correlators (OTOCs), whose measurements presents a formidable experimental challenge. Here we report on a method for the measurement of OTOCs based on the so-called two-point measurements scheme developed in the field of non-equilibrium quantum thermodynamics. The scheme is of broader applicability than methods employed in current experiments and also provides a clear-cut interpretation of quantum information scrambling in terms of non-equilibrium fluctuations of thermodynamic quantities such as work. Furthermore, we provide a numerical example on a spin chain which highlights the utility of our thermodynamic approach when understanding the differences between integrable and ergodic behavior. We also discuss connections to some recent experiments.

Figures (2)

• Figure 1: The Wing-flap protocol
• Figure 2: Shown here are (a) the time dependent mean and (b) second moment of the work distribution for the quench protocol described in the text. (c) shows the real part of the OTOC $F_{e^{iuO},W}(\tau)$, for $u=1$. Here we focus on a chain of $9$ spins at inverse temperature $\beta=0.1$ contrasting both integrable and non-integrable dynamics. We use the model and parameters specified in kim2013ballistic ($J=1,g=0.90450849,h=0.8090169$)