Watermarking AI text has fundamental information-theoretic limits: attributing text to users costs logarithmic tokens per user, and there's an unavoidable gap where text is provably machine-made but can't be attributed to anyone.
This paper analyzes watermarks in AI-generated text from an information theory perspective, establishing fundamental limits on what watermarks can do. It proves that attributing text to one of N users requires Θ(log N/h) tokens (where h is entropy rate), and shows detection, attribution, payload extraction, and localization form a 'forensic ladder' with different sample complexity costs.