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.

Automated summary

In this paper, we derive tight upper bounds for loss-tolerance thresholds in different linear-optical quantum information processing settings by considering the probabilistic nature of linear optical Bell measurements. We show analytically that linear optics can achieve the fundamental loss threshold imposed by the no-cloning theorem, which is less strict than the widely assumed constraint.