Quantum-information capacities and inequalities for depolarizing channels

Determine the quantum communication capacity, the distillable entanglement of the Choi state, and the exact tensorization behavior of hypercontractive and logarithmic Sobolev inequalities for quantum depolarizing channels in general.

Background

The paper situates its study of classical communication within broader unresolved questions about quantum depolarizing channels. It explicitly identifies the quantum communication capacity, the distillable entanglement of the channel's Choi state, and exact tensorization of hypercontractive and logarithmic Sobolev inequalities as fundamental questions that remain unresolved. These topics concern whether entanglement and coherent operations across multiple channel uses provide advantages for quantum-information tasks beyond the classical capacity setting addressed in the paper.

References

Even the simple and highly symmetric quantum depolarizing channel leaves fundamental questions unresolved, including the quantum communication capacity, distillable entanglement of its Choi state, and the exact tensorization of hypercontractive and logarithmic Sobolev inequalities in general.

— Approximate majorization and high-order capacity of quantum depolarizing channels  (2609.37240 - Song et al., 29 Sep 2026) in Section 1, Introduction

Depolarizing noise is a fundamental and well-studied error model in quantum information processing, yet the quantum capacity of this channel is unknown.

— A depolarizing choir sings in Gaussian harmony  (2609.39747 - Ahmed et al., 30 Sep 2026) in Introduction