  We consider the task of deterministically entangling two remote qubits using
joint measurement and feedback, but no directly entangling Hamiltonian. In
order to formulate the most effective experimentally feasible protocol, we
introduce the notion of average sense locally optimal (ASLO) feedback
protocols, which do not require real-time quantum state estimation, a difficult
component of real-time quantum feedback control. We use this notion of
optimality to construct two protocols which can deterministically create
maximal entanglement: a semiclassical feedback protocol for low efficiency
measurements and a quantum feedback protocol for high efficiency measurements.
The latter reduces to direct feedback in the continuous-time limit, whose
dynamics can be modeled by a Wiseman-Milburn feedback master equation which
yields an analytic solution in the limit of unit measurement efficiency. Our
formalism can smoothly interpolate between continuous-time and discrete-time
descriptions of feedback dynamics, and we exploit this feature to then derive a
superior hybrid protocol for arbitrary non-unit measurement efficiency that
switches between quantum and semiclassical protocols. Finally, we show using
simulations incorporating experimental imperfections that deterministic
entanglement of remote superconducting qubits may be achieved with current
technology using the continuous-time feedback protocol alone.
