No-Go Theorems for Universal Entanglement Purification

TL;DR

This paper proves fundamental limitations on universal entanglement purification protocols using local operations, showing they cannot exist for all two-qubit states under certain conditions, unlike more general operations.

Contribution

It establishes no-go theorems demonstrating the impossibility of universal entanglement purification with local operations and classical communication.

Findings

No universal n-to-1 EPP with LOCC for all two-qubit states.

Universal EPPs exist with PPT operations, beyond LOCC.

Bilocal Clifford EPPs cannot be universal even at high fidelities.

Abstract

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.