Source-linked AI summary
A No-Go Theorem for Gaussian Quantum Error Correction
Julien Niset, Jaromir Fiurasek, Nicolas J. Cerf
TL;DR
The paper addresses whether Gaussian errors can be corrected using only Gaussian operations, an unresolved question motivated by the connection between error correction and entanglement distillation. It introduces entanglement degradation for single-mode Gaussian channels and proves, via that connection, that Gaussian encoding and decoding cannot reduce it, establishing a Gaussian error-correction no-go theorem.
Problem
Whether Gaussian errors can be corrected using Gaussian operations alone remained unresolved, despite the connection between quantum error correction and entanglement distillation.
Method
The paper introduces entanglement degradation for single-mode Gaussian channels and connects Gaussian error-correcting codes to one-way Gaussian protocols through Gaussian channel-state isomorphism.
Results
Gaussian encoding and decoding operations cannot reduce a channel’s entanglement degradation, so Gaussian error correction cannot improve Gaussian-state transmission through a Gaussian channel.
Takeaways & Limitations
The result establishes a no-go theorem for correcting Gaussian errors with Gaussian operations only and complements the impossibility of Gaussian entanglement distillation.
Takeaways & Limitations
The proof focuses on deterministic Gaussian completely positive maps, which describe the most common practical setting.
Abstract
from arXiv · showhide
It is proven that Gaussian operations are of no use for protecting Gaussian states against Gaussian errors in quantum communication protocols. Specifically, we introduce a new quantity characterizing any single-mode Gaussian channel, called entanglement degradation, and show that it cannot decrease via Gaussian encoding and decoding operations only. The strength of this no-go theorem is illustrated with some examples of Gaussian channels.