Collective Recovery of Quantum Communication under Projective Constraints

We study quantum communication when projections on the original input reproduce measurement statistics exactly. Additional readable strategy labels count toward the quantum output dimension. Collective implementations recover the ideal rate for commuting effects within the original output dimension. For binary weak measurements, the optimal total loss has leading term one half of log2(n), even for coherent correlated sources and arbitrary projectors. At the noncommuting trine boundary, every exact collective projectively simulable implementation is entanglement breaking. This first preprint version includes the main manuscript, Supplemental Material with analytic proofs, and a self-contained selected-code reproducibility bundle (four small-CPU scripts, reference figure data, and fresh-run verification). The work has not undergone journal peer review.