Howard Barnum, Carl Philipp Gaebler, Alexander Wilce (2009), Foundations of Physics 43(12):1411–1427 (2013; online 2013-10-31); arXiv preprint first — ARXIV-0912.5532
Key takeaways
- In any probabilistic theory where every system can steer its own states (universal self-steering), state spaces are homogeneous and weakly self-dual. Upgrade weak to strong self-duality and add local tomography and qubits, and Koecher–Vinberg plus Hanche-Olsen force finite-dimensional complex C*-algebraic quantum theory.
Seeded from the abstract and a skim, before the reading in NOTE-082. What follows is what the work says about itself.
A bipartite state steers its marginal if, for any decomposition of that marginal into an ensemble, some measurement on the other side prepares exactly that ensemble with the right probabilities. Schrödinger observed that pure quantum states always allow this. The authors show that for weakly self-dual state spaces (isomorphic to their duals, though not canonically), requiring every state of a system to be steerable from a composite of two copies of it amounts to requiring that the state cone be homogeneous. If the space is genuinely self-dual, the Koecher–Vinberg theorem makes it the self-adjoint part of a formally real Jordan algebra, which is very close to quantum mechanics.
Standing in the record
Filed from the survey of 2026-09-25 of work the anthology set aside as out of scope (tier C): 490 seconds of active reading over 3 sessions in the papers-feed tracker. It was filed Deferred, unread. NOTE-082 is the close reading of 2026-09-25, and it placed the work: Active — a short, readable and mostly proved link from an operational feature (ensemble steering) to cone geometry (homogeneity, weak self-duality). It remains a standard reference for the steering route in GPT reconstructions. Read it with the open weak/strong self-duality gap and the thin argument for Prop. 5.7 in view.
When seeded, before the reading in NOTE-082, the entry gave a priority for a deeper reading: low — Owner time is moderate (t=490, n=3). The skim captures the logical chain, and what remains is technical convex geometry best read next to the GPT review.
What the seeding asked a deeper reading to check (NOTE-082 is that reading):
- It is a clean example of a reconstruction strategy: pick an information-theoretic feature (steering) and derive geometry (homogeneous, self-dual cones). It is relevant to the GPT cluster (c21) and to ψ-ontology debates (c20, c19).
- Check whether the weak/strong self-duality gap has since been closed (the authors cite one strategy as [32]) and whether the 2013 journal version differs from arXiv v2.
Access when seeded: arXiv abs page (v1 30 Dec 2009, v2 4 Mar 2010) and full PDF of v2 (24 pp.) read directly: introduction, section structure, §4 opening and §6 conclusion. The arXiv page lists no DOI. I found the journal version by a Crossref bibliographic search: same title and authors, Foundations of Physics 43(12):1411–1427, online 2013-10-31. I did not compare it with v2.