No deterministic purification for two copies of a noisy entangled state.
We consider whether two copies of a noisy entangled state can be purified into a single copy with less noise using local operations and classical communication. We show that this is impossible to achieve with certainty when the states form a one parameter twirlable family (i.e., a local twirling operation exists 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 purified. Furthermore, due to the nature of the proof, it will hold not only in quantum theory, but in any nonlocal probabilistic theory. Hence two noisy Popescu-Rohrlich boxes (hypothetical devices more nonlocal than any quantum state) also cannot be purified.
Short
Anthony J
AJ
DAMTP, center for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WA, United Kingdom.