In recent years, physicists have been trying to better understand how quantum information spreads in systems of interacting particles—a phenomenon often referred to as "scrambling." Scrambling in closed systems, physical systems that can only exchange energy with degrees of freedom within the system, is a characteristic feature of chaotic many-body quantum dynamics.

In open systems, which can exchange both energy and matter with their surroundings, scrambling is influenced by various additional factors, including noise and errors. While the effects of these additional influences are well-documented, leading for example to decoherence, how they affect scrambling remains poorly understood.

Two researchers from the University of California Berkeley (UC Berkeley) and Harvard University recently introduced a new framework, published in Physical Review Letters, that provides a universal picture for how information scrambling occurs in open quantum systems. Their framework offers a particularly simple viewpoint on how to understand and model the propagation of errors in an open quantum system and might already help to explain some previously puzzling observations gathered in magnetic resonance experiments.

"Norm and I have worked on several projects together focusing on quantum information scrambling before," Thomas Schuster, one of the researchers who carried out the study, told Phys.org.

"Some of our works focused on how to measure scrambling, and others on what scrambling might be useful for. In all of these projects, a natural question kept coming up: How is scrambling modified by errors (that is, 'open-system' dynamics) that inevitably occur in real-life experiments? Although this question was clearly important, we did not have any satisfying framework for answering it."

While exploring this question, Schuster and Yao realized that it might be helpful to consider things from an experimental perspective. This ultimately led to their recent study.

"In open-system dynamics, errors perturb the system, and we would like to know the sensitivity of our experiment to these perturbations," Schuster said. "This suggests that the sensitivity of an experiment to errors must be related to how information scrambles. Building on this initial idea, we worked to make the connection between errors and scrambling precise, and to analyze its consequences for physical systems and experiments of interest."

The key idea behind the recent study by Schuster and Yao is that information scrambling in an open system is somewhat independent of the microscopic nature of the errors themselves. Rather, it all depends on how these errors affect the so-called "operator size distributions," a characterization of the operator's complexity under time evolution.

"The dynamics of the operator size distribution determine how errors spread in a precise way," Schuster explained. "At its simplest level, this takes the form of two coupled differential equations. The input to the equations is how the distribution of operator sizes changes while the output can be thought of as a sharp prediction for how errors spread."

While some previous studies had hinted at this connection, no one had clearly and precisely formulated it so far. In doing so, Schuster and Yao found that the interplay between errors and scrambling was much more nuanced than had been previously anticipated.

"Another novel result from our work is that errors also modify the behavior of information scrambling itself," Schuster said. "This leads to an interesting interplay between errors and scrambling, described by the equations mentioned above. The outcome of this interplay depends on the nature of the dynamics themselves and can be used as an intrinsic characterization of these dynamics, in addition to predicting various properties of experiments."