No purification for two copies of a noisy entangled state

TL;DR

This paper proves that two copies of certain noisy entangled states, including Werner states and PR-boxes, cannot be deterministically purified into a single purer state using local operations, in quantum or generalized probabilistic theories.

Contribution

It establishes a no-purification no-go theorem for two copies of twirlable noisy states, extending beyond quantum theory to generalized probabilistic frameworks.

Findings

Two copies of Werner states cannot be deterministically purified.

Two copies of noisy PR-boxes cannot be purified.

The result applies in quantum and generalized probabilistic theories.

Abstract

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 purified. 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.