Catalytic Transformations of Pure Entangled States

TL;DR

This paper demonstrates that entanglement entropy fully characterizes the transformation of pure entangled states when entanglement catalysis is involved, extending its operational significance to the single-copy regime.

Contribution

It proves that entanglement entropy determines state transformations with entangled catalysts, bridging the gap between asymptotic and single-copy regimes.

Findings

Entanglement entropy characterizes state transformations with catalysts.

Operational meaning of entanglement entropy in single-copy regime.

Extension of entanglement theory to catalytic transformations.

Abstract

Quantum entanglement of pure states is usually quantified via the entanglement entropy, the von Neumann entropy of the reduced state. Entanglement entropy is closely related to entanglement distillation, a process for converting quantum states into singlets, which can then be used for various quantum technological tasks. The relation between entanglement entropy and entanglement distillation has been known only for the asymptotic setting, and the meaning of entanglement entropy in the single-copy regime has so far remained open. Here we close this gap by considering entanglement catalysis. We prove that entanglement entropy completely characterizes state transformations in the presence of entangled catalysts. Our results imply that entanglement entropy quantifies the amount of entanglement available in a bipartite pure state to be used for quantum information processing, giving asymptotic results an operational meaning also in the single-copy setup.