Necessary conditions on entanglement catalysts

TL;DR

This paper establishes a lower bound on the dimension of entanglement catalysts needed for pure state transformations under entanglement-assisted local operations, using generalized concurrence monotones.

Contribution

It introduces a lower bound for catalyst dimension based on generalized concurrence monotones and offers tools for deriving additional conditions on catalysts.

Findings

Lower bound on catalyst dimension derived

Bound expressed via generalized concurrence monotones

Tools for further catalyst condition analysis provided

Abstract

Given a pure state transformation $\psi\mapsto\phi$ restricted to entanglement-assisted local operations with classical communication, we determine a lower bound for the dimension of a catalyst allowing that transformation. Our bound is stated in terms of the generalised concurrence monotones (the usual concurrence of two qubits is one such monotone). We further provide tools for deriving further conditions upon catalysts of pure state transformations.