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An unprecedented positron average current is required to fit the luminosity demands of future $e^+e^-$ high energy physics colliders. In addition, in order to access precision-frontier physics, these machines require positron polarization to enable exploring the polarization dependence in many HEP processes cross sections, reducing backgrounds and extending the reach of chiral physics studies beyond the standard model. The ILC has a mature plan for the polarized positron source based on conversion in a thin target of circularly polarized gammas generated by passing the main high energy e-beam in a long superconducting helical undulator. Compact colliders (CLIC, C3 and advanced accelerator-based concepts) adopt a simplified approach and currently do not plan to use polarized positrons in their baseline design, but could greatly benefit from the development of compact alternative solutions to polarized positron production. Increasing the positron current, the polarization purity and simplifying the engineering design are all opportunities where advances in accelerator technology have the potential to make a significant impact. This white-paper describes the current status of the field and provides R\&D short-term and long-term pathways for polarized positron sources.