No-Go Theorems for Universal Entanglement Purification
Allen Zang, X. Chen, Eric Chitambar, Martin Suchara, Tian Zhong · Physical Review Letters · 2025
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 input-independent 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 impossible by any bilocal Clifford EPP even when restricted to states with fidelities above an arbitrarily high threshold.