A Qubit–Qutrit Equivalence for Centrally Symmetric Two-Query Quantum Correlations

We establish a qubit–qutrit equivalence for centrally symmetric prepare-and-measure correlations involving two fixed binary queries and no shared randomness between preparation and measurement devices. For arbitrary pairs of Hermitian contractions on a three-dimensional Hilbert space, we prove a spectral-domination result that implies the following: any centrally symmetric family of target expectation pairs approximable by two binary POVMs on a qutrit, within a common compact convex centrally symmetric tolerance, is equally approximable using two fixed projective measurements on a qubit. As an exact consequence, for the four rectangular targets (±a, ±b), the optimal worst-cell total-variation error in dimensions two and three is ε₂ = ε₃ = max{0, [a + b − √(2 − (a − b)²)] / 4}, whereas dimension four permits exact reproduction. In particular, a qutrit with arbitrary binary POVMs cannot improve upon the optimal qubit worst-case success probability of (1 + 1/√2)/2 for the 2-to-1 random-access code without shared randomness. The proof uses spectral subspace intersection in dimension three and does not require the measurement operators to possess common reducing subspaces. Explicit counterexamples establish the importance of the dimensional and operational assumptions. The results provide a mathematical characterization of quantum carrier-dimension constraints, with applications to prepare-and-measure correlations and operationally recoverable historical information. Status: Research preprint, prepared for independent peer review. Not peer-reviewed. Reproducibility: Supplementary proofs, exact symbolic certificates, verification scripts and a SHA-256 manifest accompany the manuscript.