Discriminating idempotent quantum channels

2026-03-30

AI Summary

This work investigates the asymptotic binary discrimination of idempotent quantum channels, focusing on cases either lacking a common invariant state or admitting a shared full-rank invariant state. By introducing an image inclusion condition and leveraging sandwiched Rényi cb-divergences, GNS symmetry, and peripheral projection techniques, the study establishes the strong converse property for such channels for the first time. Under the image inclusion condition, single-letter closed-form expressions are derived for the Stein, Chernoff, and strong converse error exponents, demonstrating the absence of any adaptive advantage; otherwise, perfect asymptotic distinguishability is achievable. Furthermore, it is shown that for GNS-symmetric channels, the discrimination rate after repeated self-composition converges exponentially to that of the corresponding idempotent peripheral projection.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Game Theory and Economic Paradigms: Adversarial Learning
• Machine Learning: Adversarial Learning & Robustness

Application Category

• Security and Privacy: Large-scale security measurements
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs

Abstract

We study binary discrimination of idempotent quantum channels. When the two channels share a common full-rank invariant state, we show that a simple image inclusion condition completely determines the asymptotic behavior: when it holds, a broad family of channel divergences collapse to a closed-form, single-letter expression, regularization is unnecessary, and all error exponents (Stein/Chernoff/strong-converse) are explicitly computable with no adaptive advantage. Crucially, this yields the strong converse property for this channel family, which is an important open problem for general channels. When the inclusion fails, asymmetric exponents become infinite, implying perfect asymptotic discrimination. We apply the results to GNS-symmetric channels, showing discrimination rates for large number of self iterations converge exponentially fast to those of the corresponding idempotent peripheral projections. If the two channels do not share a common invariant state, we provide a single-letter converse bound on the regularized sandwiched Rényi cb-divergence, which suffices to establish a strong converse upper bound on the Stein exponents.

Problem

• idempotent quantum channels
• binary discrimination
• asymptotic behavior
• error exponents
• invariant state

Innovation

• idempotent quantum channels
• strong converse
• channel discrimination
• image inclusion condition
• sandwiched Rényi divergence