Gaussian mean width strong converse bound on the classical identification capacity of quantum channels
2026-06-03 • Information Theory
Information Theory
AI summaryⓘ
The authors developed a new way to calculate a limit (called a strong converse bound) on how much classical information can be identified using quantum channels. They use a special geometry to measure differences between outputs and apply mathematical tools to estimate how complex the output space is. This approach leads to a clearer and computable bound, improving upon previous results for certain quantum channels like depolarizing and erasure channels. Their method also allows for extensions to other geometric settings in quantum information.
Quantum channelsClassical identification capacityStrong converse boundTrace distanceEuclidean geometrySudakov's inequalityGaussian mean widthOperator normSemidefinite programmingDepolarizing channel
Authors
Satvik Singh
Abstract
We establish a single-letter and efficiently computable strong converse bound on the classical identification capacity of quantum channels. By equipping the $n$-fold channel output space with a product state-weighted $σ$-Euclidean geometry, we allow trace-distance separation constraints for identification codes to be controlled by Euclidean covering estimates. Using Sudakov's inequality, we bound the covering numbers of the $n$-fold channel outputs via their Gaussian mean widths in the weighted geometry, whose exponential growth in $n$ is governed by the operator norm of a single-letter positive operator. Upon optimizing over all weighing states $σ$, this yields a strong converse bound on the identification capacity of the channel, which also admits a semidefinite representation. Our method improves the best known converse bounds on the identification capacity of several important examples, such as depolarizing, Pauli, erasure, and amplitude damping channels. We also discuss extensions of this method to more general Euclidean geometries on the output space.