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Recent work has shown that use of quantum feedback can significantly enhanceboth the speed and success rate of measurement-based remote entanglementgeneration, but it is generally unknown what feedback protocols are optimal forthese tasks. Here we consider two common measurements that are capable ofprojecting into pairwise entangled states, namely half- and full-paritymeasurements of two qubits, and determine in each case a globally optimalprotocol for generation of entanglement. For the half-parity measurement, werederive a previously described protocol using more general methods and provethat it is globally optimal for several figures of merit, including maximalconcurrence or fidelity, and minimal time to reach a specified concurrence orfidelity. For the full-parity measurement, we derive a protocol for rapidentanglement 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 tothe Bloch vector length of an effective qubit. This mapping allows us to proveseveral optimality results for feedback protocols with full-paritymeasurements. We further show that our full-parity protocol transfersentanglement optimally from one qubit to the other amongst allmeasurement-based schemes. The methods developed here will be useful forderiving feedback protocols and determining their optimality properties in manyother quantum systems subject to measurement and unitary operations.

What is the optimal way to prepare a Bell state using measurement and feedback?