The “butterfly effect” is a term from nonlinear dynamics, which is a subdomain of physics. It occurs in systems that meet three requirements: the output is not always proportional to the input (“nonlinear”), the progression is dependent on time, but is a function of only the original state (“dynamic”), and randomness is not a factor (“deterministic”: if A, then B). When these three conditions are met, a small change to the initial conditions can lead to large changes in the results. The phrase was coined by the meteorologist Edward Lorenz, who was referring to a butterfly flapping its wings in the Amazon rainforest being able to influence the weather in Texas.

The phrase is generally used today when a seemingly insignificant cause can have a large effect. The quantum world does not exhibit deterministic behavior, however, so you can’t really speak of a butterfly effect there. There are, however, some parallels. Researchers are studying how quickly certain effects propagate in certain quantum systems. The most important effect here is decoherence, that is, the inevitable, but undesired disappearance of a fragile quantum state in favor of the normal world. To that end, you need to understand that quantum states unfortunately have the tendency to dissipate, primarily through interactions. This makes it difficult to build useful things like quantum computers, for example. The quantum state is ordered; decoherence spreads chaos, so this process is also called a “butterfly effect.”

How the butterfly effect progresses in quantum effects depends on the specific system. Determining this progression for individual systems is the focus of current research (for instance, for diffusive metals or for cooled cesium atoms). An interesting technique is used in many systems: if certain quantum operations are performed on these systems, they can be transformed into an earlier state. If you wanted to describe this in popular terms (like, for example, this press release from the Los Alamos National Laboratory, which was very popular in some media circles), you could say: the system time-traveled to the past.

So, what would happen if the system is then deliberately disturbed in the past? This question is the topic of a paper in the Phys. Rev. Letters. There, part of the quantum system is subjected to a measurement in the past, so that it loses its quantum properties. If the same quantum operations that were used to send a system back in time are then applied to the system again, it returns to the present. The surprising result: the system heals itself, that is, it has all of its quantum properties again (or at least many of them). This works better the further the system was sent back into the past in the first place.