Limits for Entanglement Measures

The basic principle of entanglement processing says that entanglement cannot increase under local operations and classical communication. Based on this principle, we show that any entanglement measure $E$ suitable for the regime of a high number of identically prepared entangled pairs satisfies $E_D\le E\le E_F$, where $E_D$ and $E_F$ are the entanglement of distillation and formation, respectively. Moreover, we exhibit a theorem establishing a very general form of bounds for distillable entanglement.