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

• DOI: 10.1103/prxquantum.4.040322
• Publication Date: 2023-11-06T16:12:05Z
• Authors: Paul Hilaire; Yaron Castor; Edwin Barnes; Sophia E. Economou; Frédéric Grosshans
• Keywords: Quantum Physics; Physics; QC1-999; FOS: Physical sciences; Integrated optics; Quantum error correction; 01 natural sciences; QA76.75-76.765; [PHYS.QPHY]Physics [physics]/Quantum Physics [quant-ph]; 0103 physical sciences; Computer software; Quantum communication; Quantum Physics (quant-ph); Quantum foundations; Quantum information theory

17pages, 14 figures<br/>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, following 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 non-adaptive Bell measurements.<br/>