Linear Optical Logical Bell State Measurements with Optimal Loss-Tolerance Threshold

(Received February 2023; May 2023; accepted September 2023; published 2023) Quantum threshold theorems impose hard limits on the hardware capabilities to process quantum information. We derive tight and fundamental upper bounds to loss-tolerance thresholds in different linear-optical quantum information processing settings through an adversarial framework, taking into account the intrinsically probabilistic nature of linear optical Bell measurements. For logical Bell state measurements-ubiquitous operations in photonic quantum information-we demonstrate analytically that linear optics can achieve the fundamental loss threshold imposed by the no-cloning theorem even though, fol-lowing the work of Lee et al. [Phys. Rev. A 100, 052303 (2019)] the constraint was widely assumed to be stricter. We spotlight the assumptions of the latter publication and find their bound holds for a logical Bell measurement built from adaptive physical linear-optical Bell measurements. We also give an explicit even stricter bound for nonadaptive Bell measurements.