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 nonadaptive Bell measurements.
- Received 21 February 2023
- Revised 22 May 2023
- Accepted 22 September 2023
DOI:https://doi.org/10.1103/PRXQuantum.4.040322
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.
Published by the American Physical Society
Physics Subject Headings (PhySH)
Popular Summary
A critical issue in photonic quantum technologies are photon losses which have long been a major source of errors in quantum systems. However, there's good news - quantum error correction can effectively rectify these errors. Photonic quantum information processing relies heavily on linear optical interferometers and detectors. Among the essential operations is the Bell state measurement, which is a key intrinsic element of photonic quantum processing.
In this work, we have conducted a meticulous assessment of the maximum allowable loss when employing quantum error correcting codes in linear-optical quantum information processing, with a specific focus on logical Bell state measurements. We established three distinct boundaries based on the type of optical setup: static linear-optical configurations, adaptive setups utilizing solely physical Bell state measurements, and adaptive setups combining physical Bell states with single qubit measurements.
This work opens up new horizons for the practical implementation of quantum error correction in photonic systems. For instance, it highlights the necessity of adaptive measurement configurations, where the measurements of subsequent photonic qubits should depends on past measurement results. This approach enhances the system's tolerance to losses, unlocking the complete potential of quantum information processing.
