Bell state measurements in quantum optics: a review of recent progress and open challenges

Abstract Bell state measurements, which project bipartite states onto the maximally entangled Bell basis, are central to a wide range of quantum information processing tasks, including quantum teleportation, entanglement swapping, and fusion-gate quantum computation. In photonic platforms, where information is encoded in optical degrees of freedom, the realization of efficient Bell state measurements is particularly challenging, especially when constrained to linear optical elements. In this review, we provide a comprehensive examination of existing proposals for the implementation of Bell state measurements, highlighting their fundamental limitations and the strategies developed to overcome them. Moreover, we survey recent advances and discuss open challenges, with a particular focus on Bell state measurements for high-dimensional systems, an area of growing interest due to its relevance for quantum repeaters and scalable quantum networks.