Enhanced quantum capacity thresholds from symmetry

2026-05-09

AI Summary

Determining the quantum capacity threshold of depolarizing and Pauli channels has long been hindered by a substantial gap between upper and lower bounds and limited progress. This work overcomes this stagnation by optimizing the coherent information of rank-two states within the fully symmetric subspace and leveraging group representation theory to demonstrate a significant reduction in environment entropy. For the first time in eighteen years, it breaks through the capacity threshold of the depolarizing channel, achieving an improvement exceeding the cumulative gains of all prior advances since the hashing bound. Beyond extending the existing representation-theoretic framework to more general symmetric structures, the study further uncovers the critical role of code degeneracy as a key mechanism for enhancing quantum capacity.

Abstract

The quantum capacity captures the value of a quantum channel for transmitting quantum information, establishing the fundamental limits on quantum communication. In spite of its central role in quantum information theory, the quantum capacity of most channels is unknown, with wide gaps between the best upper and lower bounds. Even deciding whether a channel has nonzero capacity -- finding its capacity threshold -- is difficult. In this paper we report significant increases in the capacity thresholds of two prototypical noise models: the depolarizing channel and Pauli channels. In the case of the depolarizing channel, this is the first improvement in 18 years, giving a bigger increase beyond the hashing bound than all previous improvements combined. Our starting point is the representation theoretic framework recently proposed by Bhalerao and Leditzky (2025) to compute coherent information for special permutation invariant states. We generalize their framework to the full symmetric subspace, which allow us to optimize coherent information over rank two states in that space. A representation theoretic calculation shows that exponentially many Kraus operators of the channel annihilate the symmetric space, corresponding to a massive decrease in environment entropy for states on the symmetric space compared to the maximally mixed state. This explains the enhanced coherent information as a manifestation of degeneracy for the resulting codes.

Problem

• quantum capacity
• capacity threshold
• depolarizing channel
• Pauli channels
• coherent information

Innovation

• quantum capacity
• symmetric subspace
• coherent information
• representation theory
• depolarizing channel