Theory of remote entanglement via quantum-limited phase-preserving amplification

We show that a quantum-limited phase-preserving amplifier can act as a which-path information eraser when followed by detection of both quadratures. This beam splitter with gain implements a continuous joint measurement on the signal sources. As an application, we propose heralded 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 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.