  Conditional detection is an important tool to extract weak signals from a
noisy background and is closely linked to heralding, which is an essential
component of protocols for long distance quantum communication and distributed
quantum information processing in quantum networks. Here we demonstrate the
conditional detection of time-bin qubits after storage in and retrieval from a
photon-echo based waveguide quantum memory. Each qubit is encoded into one
member of a photon-pair produced via spontaneous parametric down conversion,
and the conditioning is achieved by the detection of the other member of the
pair. Performing projection measurements with the stored and retrieved photons
onto different bases we obtain an average storage fidelity of 0.885 \pm 0.020,
which exceeds the relevant classical bounds and shows the suitability of our
integrated light-matter interface for future applications of quantum
information processing.
