  We consider protocols to generate quantum entanglement between two remote
qubits, through joint time-continuous detection of their spontaneous emission.
We demonstrate that schemes based on homodyne detection, leading to diffusive
quantum trajectories, lead to identical average entanglement yield as
comparable photodetection strategies; this is despite substantial differences
in the two-qubit state dynamics between these schemes, which we explore in
detail. The ability to use different measurements to achieve the same ends may
be of practical significance; the less-well-known diffusive scheme appears far
more feasible on superconducting qubit platforms in the near term.
