(Not a Teacher)
Originally, a herald was a member of a distinguished person's entourage (a noble, king, knight, etc.) who went ahead of the party and announced their arrival, usually with much fanfare. 'Harbinger' is a similar concept, but he brings news of a more 'fateful' variety.
You could replace it with 'foretold', 'predicted', 'hailed', or perhaps 'anticipated', though 'heralded' sounds more grand than either one.
However, the way they use 'heralded entanglement' suggests it may be a technical term here. However, I can't find it in a dictionary, and it's not really explained in the article itself. Maybe they just mean 'heralded' in the sense of 'hailed' or 'predicted', but one would think they'd have used a 'the' before 'heralded' if that's what they meant.