Speed limits on quantum dynamics with long-range interactions*

In 1972, Lieb and Robinson proved that quantum information propagates with a finite velocity in quantum many-body systems with local interactions.  Yet most physically realized systems have long-range interactions, that decay as a power law with the distance between two particles.  Are there still meaningful speed limits on the propagation of quantum information in these physically realized systems?  

The past two years have seen significant progress in resolving this longstanding question.  I will describe (essentially) optimal constraints on the growth of quantum correlators in arbitrary systems with long-range interactions, and explain how to send quantum information and prepare entangled states as fast as possible.  I will then describe the existence of a hierarchy of speed limits with long-range interactions, emphasizing that the "Lieb-Robinson speed limit" may not ultimately constrain quantum dynamics in experimentally meaningful applications. I will conclude with a brief outlook for future important problems that remain open.