Linear optical logical Bell state measurements with optimal loss-tolerance threshold

TL;DR

This paper establishes fundamental upper bounds on loss-tolerance thresholds for linear optical logical Bell state measurements, showing that optimal thresholds are achievable even under probabilistic constraints, with implications for photonic quantum computing.

Contribution

The paper derives tight upper bounds on loss-tolerance thresholds for linear optical Bell measurements, clarifying the fundamental limits and correcting previous assumptions.

Findings

Linear optics can reach the no-cloning limit for loss-tolerance thresholds.

Adaptive measurements meet the fundamental loss threshold, non-adaptive measurements have stricter bounds.

Analytical bounds are provided for different measurement strategies.

Abstract

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.