Nature Reviews Physics (2020) https://www.nature.com/articles/s42254-020-0193-5 Published online 25 June 2020

In the original version of the article, Figure 1 was missing the credit line, “The image representing entanglement is adapted with permission from Paul Kwiat and Michael Reck”. Table 1 incorrectly stated that the 3d-GHZ is a Class II state. The 3d-GHZ is a Class III state. These have been corrected in the HTML and PDF versions of the manuscript.