  Entanglement purification allows the creation of qubit pairs of arbitrarily
high fidelity with respect to a maximally entangled state, starting from a
larger number of low-fidelity pairs. Purification requires quantum memory, a
role for which electron spins are well suited. However, using existing
recurrence protocols involving symmetric local two-qubit operations for spin
qubits turns out to be rather unpractical. We present an efficient purification
protocol requiring only a single pulsed Heisenberg- or XY-type exchange
interaction between two qubit pairs. In contrast to known protocols, we allow
for asymmetric bilateral two-qubit operations where the two communication
parties operate differently on their qubits. In the optimal version of our
protocol, the local two-qubit interactions in the case of Heisenberg exchange
correspond to the $\sqrt{\mathrm{SWAP}}$ gate and its inverse.
