An unreviewed preprint posted to arXiv claims to fully resolve a long-standing question in quantum information theory: how much classical communication is required to exactly simulate quantum communication and Bell-nonlocal correlations at every Hilbert-space dimension? The authors report that the answer undergoes a sharp qualitative transition at dimension four. Below that threshold, finite classical resources suffice; at and above it, no finite amount of classical communication can replicate the statistics of quantum channels or entangled ququart measurements, even when the simulating parties share unlimited randomness.
The result extends the only previously solved case — the qubit, which was known to require exactly two classical bits — and settles both the communication-simulation and correlation-simulation problems in a unified framework. Notably, the transition does not appear at dimension three as intuition might suggest. The authors construct an explicit protocol that simulates a qutrit channel using 357 classical bits, and from it derive a simulation of all correlations producible by two entangled qutrits. The jump to infinity at dimension four is therefore not a gradual divergence but a discrete qualitative change in the classical cost of quantum behavior.
If the claims survive peer review, the work would close open problems that have attracted significant effort over more than two decades, while raising new structural questions about why the classical-simulation complexity of quantum systems remains finite through dimension three and then becomes infinite. The paper has not yet been peer-reviewed, and readers should treat the results accordingly until independent verification is available.