  An entanglement purification protocol (EPP) aims to transform multiple noisy
entangled states into a single entangled state with higher fidelity. In this
work we consider EPPs that always yield an output fidelity no worse than each
of the original noisy states, a property we call universality. We prove there
is no $n$-to-1 EPP implementable by local operations and classical
communication that is universal for all two-qubit entangled states, whereas
such an EPP is possible using more general positive partial
transpose-preserving (PPT) operations. We also show that universality is not
possible by bilocal Clifford EPPs even when restricted to states with
fidelities above an arbitrarily high threshold.
