  We show that a quantum-limited phase-preserving amplifier can act as a
which-path information eraser when followed by heterodyne detection. This 'beam
splitter with gain' implements a continuous joint measurement on the signal
sources. As an application, we propose heralded concurrent remote entanglement
generation between two qubits coupled dispersively to separate cavities.
Dissimilar qubit-cavity pairs can be made indistinguishable by simple
engineering of the cavity driving fields providing further experimental
flexibility and the prospect for scalability. Additionally, we find an analytic
solution for the stochastic master equation, a quantum filter, yielding a
thorough physical understanding of the nonlinear measurement process leading to
an entangled state of the qubits. We determine the concurrence of the entangled
states and analyze its dependence on losses and measurement inefficiencies.
