Quantum entanglement can be distilled: given many copies of a weakly entangled state, you can produce fewer copies of a strongly entangled state using only local operations and one-way classical communication. The rate at which this is possible — the one-way distillable entanglement — is a fundamental measure of quantum correlation. But computing it requires optimizing over an infinite number of copies (a “regularized” formula), which is generally intractable.
For degradable states — states where the environment's information is a degraded version of what the receiver gets — a single-letter formula exists: you only need to optimize over one copy. But most states aren't degradable. Ahmed, Smith, and Wu (arXiv: 2603.23417) find three families of non-degradable states that nonetheless have single-letter formulas.
The trick: weaken the degradability condition. “Regularized less-noisy” and “informationally degradable” are new conditions, strictly weaker than degradable but strong enough to guarantee that the multi-copy optimization collapses to a single-copy one. The entanglement formula doesn't simplify because the state is simple — it simplifies because the state has just enough structure to prevent the multi-copy correlations from helping.
Additional results: orthogonally flagged mixtures (states built from orthogonal components) are stable under these conditions, and a generalized spin-alignment principle helps minimize the conditional entropy.
The through-claim: computability is a property of structure, not of simplicity. Non-degradable states can have simple formulas. The single-letter condition doesn't require the state to be nice — it requires the state's structure to prevent multi-copy exploitation. The formula collapses not because one copy is enough information, but because additional copies are redundant. Redundancy, not simplicity, is what makes entanglement computable.
Ahmed, Smith & Wu, 2603.23417. Quantum information / entanglement distillation / single-letter formulas / degradability / one-way communication.