Martin Plávala (2021), Physics Reports 1033:1–64 (2023); arXiv preprint first — ARXIV-2103.07469
Key takeaways
- A self-contained, convex-geometric textbook introduction to GPTs, the operational framework containing finite-dimensional classical and quantum theory and exotic theories like boxworld (PR boxes). It proves standard results such as “the identity channel is measure-and-prepare ⇔ a universal broadcasting channel exists ⇔ the state space is a simplex (classical)”.
Seeded from the abstract and a skim, before the reading in NOTE-035. What follows is what the work says about itself.
The review introduces general probabilistic theories: operational theories that generalize finite-dimensional classical and quantum theory and also include more exotic ones, such as boxworld with its Popescu–Rohrlich boxes. It explains the basic concepts and elements of the framework in depth and proves several well-known results. It aims to be self-contained and consistent. Its main tool is convex geometry, supplemented by a diagrammatic notation used to write many equations.
Standing in the record
Filed from the survey of 2026-09-25 of work the anthology set aside as out of scope (tier C): 300 seconds of active reading over 1 session in the papers-feed tracker. It was filed Deferred, unread. NOTE-035 is the close reading of 2026-09-25, and it placed the work: Active — the best single entry point to the GPT vocabulary this record’s Spekkens-programme readings presuppose (state space, effect algebra, GPT dimension, tomographic locality, minimal/maximal tensor products, measure-and-prepare). Read §2–3, §5.1, §5.5, §6.1–6.5 and §7.1. It is not the place for restricted theories like Spekkens’ toy theory, to which §3.7 gives a single paragraph.
When seeded, before the reading in NOTE-035, the entry gave a priority for a deeper reading: medium — It is a reference work rather than an argument (t=300, n=1). Its value comes from selective reading of §3, §5 and §7 when a cluster note needs a definition, and the skim cannot substitute for that.
What the seeding asked a deeper reading to check (NOTE-035 is that reading):
- It is the reference text for the GPT vocabulary the rest of the cluster uses (c17’s self-duality and steering results, c16’s toy theory as a restricted GPT). It is the natural “start here” note.
- A deeper read should use §7.3 (steering in GPTs) alongside c17, and check how §3.7’s no-restriction hypothesis affects which results carry over to restricted theories like Spekkens’.
Access when seeded: arXiv abs page (v1 12 Mar 2021, v2 23 Aug 2021) and full PDF of v2 (76 pp.) read directly: abstract, full table of contents, §1 introduction, and the §7.1 no-broadcasting derivation with Theorem 7.7. Crossref confirms Physics Reports 1033:1–64 (Sept 2023). I did not compare the journal version with v2.