Since no one responded, I've done a little more research and found some information in the popular press that may be helpful. This article
in Technology Review is a little vague but does help to clarify a few points.
First they explain that normally entanglement is understood to violate the principle of locality by operating instantaneously over vast distances - although to some extent this can be seen as a matter of interpretation.
They then explain that it can also act in a similar fashion across time. So you could have one quantum circuit that encodes a qubit while also creating the information needed to decode it. Later, another detector in the same area of space could retrieve the information and decode the qubit.
But there's a twist. Olson and Ralph show that the detection of the qubit in the future must be symmetric in time with its creation in the past. "If the past detector was active at a quarter to 12:00, then the future detector must wait to become active at precisely a quarter past 12:00 in order to achieve entanglement," they say. For that reason, they call this process "teleportation in time".
But how is this different from ordinary existence? After all, we're all time travellers, moving into the future at the same rate. What's special about Olson and Ralph's route?
The answer is that Olson and Ralph's teleportation provides a shortcut into the future. What they're saying is that it's possible to travel into the future without being present during the time in between.