Disentanglement Cost of Quantum States

TL;DR

This paper establishes the minimal noise rate required to catalytically erase entanglement in bipartite quantum states as the regularized relative entropy of entanglement, providing a solution to a longstanding open problem.

Contribution

It identifies the exact minimal noise rate for entanglement erasure and extends the analysis to tripartite states involving the regularized relative entropy of recovery.

Findings

Minimal noise rate for entanglement erasure equals regularized relative entropy of entanglement.

Noise rate for erasing all correlations equals quantum mutual information.

Asymptotic noise rate suffices for transforming states to locally recoverable versions.

Abstract

We show that the minimal rate of noise needed to catalytically erase the entanglement in a bipartite quantum state is given by the regularized relative entropy of entanglement. This offers a solution to the central open question raised in [Groisman, PRA 72, 032317 (2005)] and complements their main result that the minimal rate of noise needed to erase all correlations is given by the quantum mutual information. We extend our discussion to the tripartite setting where we show that an asymptotic rate of noise given by the regularized relative entropy of recovery is sufficient to catalytically transform the state to a locally recoverable version of the state.