  Pure states are an important resource in many quantum information processing
protocols. However, even making a fixed pure state, say $|0\rangle$, in the
laboratory requires a considerable amount of effort. Often one ends up with a
mixed state $\rho$ whose classical description is nevertheless known. Hence it
is important to develop protocols that extract a fixed pure state from a known
mixed state. In this work, we study the problem of extracting a fixed pure
state $|0\rangle^{A'} |0\rangle^{B'}$ from a known pure state $\rho^{AB}$
distributed between two parties $A$ and $B$. Here, $A'$, $B'$ are subspaces of
$A$, $B$ and the total amount of purity extracted is $\log |A'| + \log |B'|$.
The parties can borrow local pure ancilla, apply local unitary operations and
send a message from $A$ to $B$ through a dephasing channel. If local pure
ancilla is borrowed, it must be subtracted in order to properly account for the
purity extracted. We obtain the most efficient achievable bounds on one shot
distributed purity extraction, in terms of the rate of local ancilla borrowed
by the protocol, while distilling pure qubits at the best known rate. Our
protocols borrow little to no local pure ancilla. Our bounds improve upon the
existing bounds for this problem in both one shot as well as asymptotic iid
settings. In particular they subsume all the asymptotic iid results of Devetak
and Krovi-Devetak. In addition, we derive upper bounds for the rate of
distillation in the one shot setting, which nearly match our achievable bounds.
