A depolarizing choir sings in Gaussian harmony

2026-09-30

AI Summary

This study addresses the fundamental challenge in quantum information theory of determining the noise threshold for the positive capacity of quantum depolarizing channels. By analyzing the asymptotic limit of symmetric subspaces, this work reveals the emergence mechanism of bosonic Gaussian channels, thereby establishing a rigorous theoretical connection between depolarizing and Gaussian channels. Leveraging this simplified model, the authors optimize complex coding strategies and map the results back to the original channel. Consequently, this paper derives and improves lower bounds on the noise threshold for positive capacity, deepens the theoretical understanding of symmetric codes, and provides a novel paradigm for the analysis of quantum channel capacities.

Abstract

We study the noise threshold for positive quantum capacity for the qubit depolarizing channel. We explore analytically the action of the qubit depolarizing channel on the symmetric subspaces of the input qubits, in the limit of asymptotically many uses of the channel. We observe the emergence of a bosonic Gaussian channel. Furthermore, the codes previously developed for the depolarizing channel can be translated to codes for the emergent Gaussian channel, and it is easier to further optimize these codes for the simpler emergent Gaussian channel. Translating these codes back to the depolarizing channel leads to extremely good input states for the coherent information of the depolarizing channel producing new lower bounds on the noise threshold for positive capacity. In addition to improved lower bounds on the threshold, this newly found link between depolarizing noise and Gaussian channels offers a novel perspective contributing to our understanding of these symmetric codes.

Problem

• depolarizing channel
• quantum capacity
• noise threshold
• Gaussian channel
• coherent information

Innovation

• depolarizing channel
• Gaussian channel
• symmetric subspaces
• coherent information
• quantum capacity