A No-Go Theorem for Gaussian Quantum Error Correction

TL;DR

This paper proves that Gaussian operations cannot be used to correct Gaussian errors in quantum communication, establishing a fundamental limitation known as a no-go theorem.

Contribution

The paper introduces the entanglement degradation measure and demonstrates its invariance under Gaussian encoding and decoding, proving the impossibility of Gaussian error correction.

Findings

Gaussian operations cannot improve entanglement degradation.

The no-go theorem applies broadly to Gaussian channels.

Examples illustrate the limitations in Gaussian quantum error correction.

Abstract

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.