“A quantum equivalent to Bayes’ rule” by dr_s

Audio note: this article contains 42 uses of latex notation, so the narration may be difficult to follow. There's a link to the original text in the episode description.

This post is an attempt to summarise and explain for the LW readership the contents of this paper: "Quantum Bayes' rule and Petz transpose map from the minimum change principle". It's a highly technical paper heavy on quantum mechanics formalism that took me a couple of days to unpack and digest a bit, but I think it may be important going forward. My work on it is far from done, but this is a quick introduction.

Epistemic status: I have a Physics PhD and spent about ten years working with computational quantum mechanics so hopefully I know what I'm talking about, but if anyone can peer review I'll be glad for the help.

The tagline of Astral Codex [...]

---

Outline:

(05:19) Classical derivation

(07:37) Minimum change derivation of Bayes rule

(08:34) Quantum derivation

(10:38) Crunching some numbers

(12:35) Conclusion

The original text contained 4 footnotes which were omitted from this narration.

---

First published:

August 31st, 2025

Source:

https://www.lesswrong.com/posts/qjRYvGcZrrdqyzoRY/a-quantum-equivalent-to-bayes-rule

---

Narrated by TYPE III AUDIO.