Temporal modes (TM) are field-orthogonal broadband wave-packet modes. They are a largely untapped degree of freedom for quantum information storage and retrieval in states of light. They form a natural basis for analysis of diverse quantum resources, be they pulsed photon sources or quantum memories with optical read-in/read-out channels. The chief enabling technology for TM manipulation is the Quantum pulse gate (QPG), an ideal device that can "separate" a selected TM component from an input beam with unit efficiency, whilst avoiding crosstalk from orthogonal TMs. Time ordering effects enforce a trade-off condition between these two objectives, ultimately limiting the selectivity of physical QPG implementations. This talk will present a derivation of the selectivity limit for traveling-wave nonlinear interactions, and present two means of overcoming the same: One utilizes cascaded interferometric stages to asymptotically approach unit selectivity, and the other uses nonlinear cavities with dichroism in Q-factors. The second method utilizes a very general theoretical formalism, making it applicable to myriad quantum systems from trapped-ion qubits, to atomic-ensemble broadband memories, to superconducting qubits.