Robert W. Spekkens (2014), arXiv preprint; later a chapter in “Quantum Theory: Informational Foundations and Foils” (G. Chiribella & R. W. Spekkens, eds.), Fundamental Theories of Physics, Springer (online 2015-12, DOI 10.1007/978-94-017-7303-4_4) — ARXIV-1409.5041
Key takeaways
- Imposing a single “classical complementarity” restriction (you may only know jointly the values of Poisson-commuting quadrature variables) on a classical statistical theory reproduces a large part of quantum phenomenology, so any phenomenon arising in such an “epistricted” theory should be counted only weakly nonclassical.
Seeded from the abstract and a skim, before the reading in NOTE-013. What follows is what the work says about itself.
The paper argues that much of quantum theory follows from one departure from classical physics: a fundamental limit on which probability distributions over physical states can be prepared, i.e. on what any observer can know. It surveys such “epistricted” theories for continuous and discrete degrees of freedom and shows that one restriction, classical complementarity, defined via the symplectic structure of phase space, begins to unify them. Because it applies to any classical degree of freedom it acts as a “quasi-quantization” scheme, yielding only a subset of quantum theory (and, for bits, a distorted one). The author proposes classifying quantum phenomena as weakly or strongly nonclassical according to whether they can arise in an epistricted theory.
Standing in the record
Filed by the reading-time triage of 2026-09-25: 1,615 seconds of active reading over 5 sessions in the papers-feed tracker. It was filed Deferred, unread. NOTE-013 is the close reading of 2026-09-25, and it placed the work: Active — the clearest single statement of the epistricted-theory programme, and the source of the weak/strong nonclassicality split that 2111.13727 and 2005.07161 build on; read it for §II–IV and App. A, not for Table II, which it asserts rather than derives.
When seeded, before the reading in NOTE-013, the entry gave a priority for a deeper reading: high — the owner spent the most time on this (t=1615 s), it is the foundational framing for items 17 and 71, and the skim captures the map but not the technical core of §II-III.
What the seeding asked a deeper reading to check (NOTE-013 is that reading):
- Strongest claim: the weak/strong nonclassicality split. Check the exact definition of “classical complementarity” (§II.A) and whether Table II’s placements (e.g. teleportation) rest on the stabilizer-restricted versions of those phenomena, as the text concedes.
- The odd-prime equivalence is a known result (Gross’s discrete Wigner function); the deeper read should isolate what is new here versus Spekkens 2007 toy theory and Bartlett-Rudolph-Spekkens 2012.
- ML link: none direct. Loosely, it is a worked example of “a restriction on admissible distributions generates rich structure”, and positivity of quasiprobability representations reappears in item 71; do not overstate this.
Access when seeded: arXiv abs page and full PDF (35 pp.) retrieved; read outline, §I.A-B (incl. Table II), §IV.B and conclusion. Chapter DOI found via Crossref bibliographic search (the arXiv page lists only the book DOI 10.1007/978-94-017-7303-4). arXiv export API returned HTTP 406 through the proxy, so metadata came from the abs page.