  Recent work has shown that use of quantum feedback can significantly enhance
both the speed and success rate of measurement-based remote entanglement
generation, but it is generally unknown what feedback protocols are optimal for
these tasks. Here we consider two common measurements that are capable of
projecting into pairwise entangled states, namely half- and full-parity
measurements of two qubits, and determine in each case a globally optimal
protocol for generation of entanglement. For the half-parity measurement, we
rederive a previously described protocol using more general methods and prove
that it is globally optimal for several figures of merit, including maximal
concurrence or fidelity, and minimal time to reach a specified concurrence or
fidelity. For the full-parity measurement, we derive a protocol for rapid
entanglement generation related to that of (C. Hill, J. Ralph, Phys. Rev. A 77,
014305 (2008)), and then map the dynamics of the concurrence of the state to
the Bloch vector length of an effective qubit. This mapping allows us to prove
several optimality results for feedback protocols with full-parity
measurements. We further show that our full-parity protocol transfers
entanglement optimally from one qubit to the other amongst all
measurement-based schemes. The methods developed here will be useful for
deriving feedback protocols and determining their optimality properties in many
other quantum systems subject to measurement and unitary operations.
