Complete Characterization of Entanglement Embezzlement

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.