Source
Spekkens (2005), LIT-266, §III, §IV (Eqs. 13–36), footnote 1, §VIII, §IX (NOTE-748). Schmid, Selby and Spekkens, LIT-945, §VI.C, for the Leibnizian principle (NOTE-737). Budroni et al. (2022), LIT-263, §IV.E.1–4 (restatement; the experimental report of Mazurek et al. 2016 is cited there, not read).
What was actually shown
Six pure qubit states give five decompositions of the maximally mixed state; distinguishable preparations cannot overlap in their ontic supports, and preparation noncontextuality then forces every distribution to vanish (§IV). Traditional Kochen–Specker proofs need dimension at least three, because a two-dimensional projective measurement has no non-trivial fine-grainings (§III). Budroni et al. restate the proof and note that Bell’s and Kochen & Specker’s own qubit models are preparation contextual (§IV.E.1, §IV.E.4; LIT-266 §IX already deems them contextual under its definition), and cite an experiment reporting a violation of the noncontextual bound (§IV.E.2–3). That bound, Mazurek et al.’s inequality, is derived from preparation and measurement noncontextuality together (§IV.E.2), so its violation refutes their conjunction, not preparation noncontextuality alone, and it rests on secondary procedures inferred in a GPT that assumes tomographic completeness.
Spekkens (LIT-266) also proves transformation contextuality for a qubit (§VI, App. A): six rotations about one axis give five convex decompositions of one map, and transformation noncontextuality then reproduces the §IV constraints (NOTE-748).
What this does not say
- That a qubit is Kochen–Specker contextual in the traditional sense, with sharp measurements; it is not. Cabello’s 2003 Kochen–Specker argument for a single qubit uses POVMs. Spekkens rejects it, not as mathematics, but because it assumes outcome determinism for unsharp measurements, which no assumption of noncontextuality justifies (footnote 1, §VIII).
- That preparation contextuality has been shown loophole-free; tomographic completeness is assumed (Budroni et al. §IV.E.3). LIT-266’s proofs assume exact operational equivalence and perfectly distinguishable pairs, and give no noise-robust inequality (§IX).
- Which notion is the right criterion of classicality. LIT-266 motivates it by ontological economy, with Einstein’s equivalence principle as the example (§VII), and does not name Leibniz. The later programme grounds it in a Leibnizian methodological principle (LIT-945, §VI.C). A reader may reject either. THEORY-231 states what that principle does in a no-go: within classical realism, a noncontextuality no-go refutes Leibnizian representations, not realist ones as such.