Complete Characterization of Entanglement Embezzlement

Abstract

Using local operations and classical communication (LOCC), entanglement can be manipulated but not created. However, entanglement can be $embezzled$. In this work, we completely characterize universal embezzling families and demonstrate how this singles out the original family introduced by van Dam and Hayden. To achieve this, we first give a full characterization of pure to mixed state LOCC-conversions. Then, we introduce a new conversion distance and derive a closed-form expression for it. These results might be of independent interest.