  Purifying noisy entanglement is a protocol which can increase the
entanglement of a mixed state (as a source)at expense of the entanglement of
others(as an ancilla)by collective measurement. A protocol with which one can
get a pure entangled state from a mixed state is defined as purifying mixed
states. We address a basic question: can one get a pure entangled state from a
mixed state? We give a necessary and sufficient condition of purifying a mixed
state by fit local operations and classical communication and show that for a
class of source states and ancilla states in arbitrary bipartite systems
purifying mixed states is impossible by finite rounds of purifying protocols.
For $2\otimes 2$ systems, it is proved that arbitrary states cannot be purified
by individual measurement. The possible application and meaning of the
conclusion are discussed.
