From the article -- Information theorists use a measure called relative entropy to compare probability distributions. It’s like measuring an abstract kind of distance: If the relative entropy between two distributions is zero, “you cannot rely on statistical analysis” to uncover the secret, said Christian Schroeder de Witt, a computer scientist at the University of Oxford who worked on the new paper. In other words, if future spies develop a perfectly secure algorithm to smuggle secrets, no statistics-based surveillance will be able to detect it. Their transmissions will be perfectly hidden.

When I got to that paragraph I knew that someone has just invented/proved "undetectable" spam. When I was doing natural language analysis with Doug Smith at Blekko to improve the crawler's ability to detect spammy web sites we used Dirichlet accumulators to generate vectors of words that were common to topics, the idea was sites with a lot off "off topic" but keyword rich text were more likely spam. The side effect was we could generate bags of words using those vectors to create pages that weren't detectable as spam, but they didn't actually say anything useful. The LLM lets you fineness that and get the best of both worlds to generate hard to detect spam. But if you can match the entropy exactly (the last remaining signal that I know of for spam) then the problem gets really really hard.