We consider whether two copies of a noisy entangled state can be transformed into a single copy of greater purity using local operations and classical communication. We show that it is never possible to achieve such a purification with certainty when the family of noisy states is twirlable (i.e. when there exists a local transformation that maps all states into the family, yet leaves the family itself invariant). This implies that two copies of a Werner state cannot be deterministically

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... . Furthermore, due to the construction of the proof, it will hold not only in quantum theory, but in any generalised probabilistic theory. We use this to show that two copies of a noisy PR-box (a hypothetical device more non-local than is allowed by quantum theory) cannot be purified.