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Entanglement swapping and heralding are at the heart of many protocols for distributed quantum information. For photons, this typically involves Bell state measurements based on two-photon interference effects. In this context, hybrid systems that combine high rate, ultra-stable and pure quantum sources with long-lived quantum memories are particularly interesting. Here, we develop a theoretical description of pulsed two-photon interference of photons from dissimilar sources to predict the outcomes of second-order cross-correlation measurements. These are directly related to, and hence used to quantify, photon indistinguishability. We study their dependence on critical system parameters such as quantum state lifetime and frequency detuning, and quantify the impact of emission time jitter, pure dephasing and spectral wandering. Our results show that for fixed lifetime of emitter one, for each frequency detuning there is an optimal lifetime of emitter two that leads to highest photon indistinguishability. Expectations for different hybrid combinations involving III-V quantum dots, color centers in diamond, 2D materials and atoms are quantitatively compared for real-world system parameters. Our work both provides a theoretical basis for the treatment of dissimilar emitters and enables assessment of which imperfections can be tolerated in hybrid photonic quantum networks.

Self-organized semiconductor quantum dots represent almost ideal two-level systems, which have strong potential to applications in photonic quantum technologies. For instance, they can act as emitters in close-to-ideal quantum light sources. Coupled quantum dot systems with significantly increased functionality are potentially of even stronger interest since they can be used to host ultra-stable singlet-triplet spin qubits for efficient spin-photon interfaces and for a deterministic photonic 2D cluster-state generation. We realize an advanced quantum dot molecule (QDM) device and demonstrate excellent optical properties. The device includes electrically controllable QDMs based on stacked quantum dots in a pin-diode structure. The QDMs are deterministically integrated into a photonic structure with a circular Bragg grating using in-situ electron beam lithography. We measure a photon extraction efficiency of up to (24$\pm$4)% in good agreement with numerical simulations. The coupling character of the QDMs is clearly demonstrated by bias voltage dependent spectroscopy that also controls the orbital couplings of the QDMs and their charge state in quantitative agreement with theory. The QDM devices show excellent single-photon emission properties with a multi-photon suppression of $g^{(2)}(0) = (3.9 \pm 0.5) \cdot 10^{-3}$. These metrics make the developed QDM devices attractive building blocks for use in future photonic quantum networks using advanced nanophotonic hardware.