From Classical to Quantum Channels: Achieving Positive Covert Rates

2026-09-28

AI Summary

This study addresses the longstanding challenge of determining conditions for achieving positive-rate covert communication over classical and quantum channels. By integrating information theory, convex geometry, and quantum channel capacity theory, the project systematically investigates the feasibility of covert communication across discrete memoryless, multiple-access, and quantum channels through comparisons of probability simplex or affine dimensions of state sets. The work reveals that an input dimension exceeding the output dimension is critical for positive-rate covertness in classical channels, proves that mixing innocent states ensures covert constraints in quantum channels, and demonstrates that multiple access relaxes covertness limitations. Ultimately, this research establishes sufficient conditions for positive-rate covert communication spanning from classical to quantum channels, confirming the feasibility of secure and covert transmission under non-trivial input ensembles.

Abstract

In this paper, we study the conditions under which covert communication at positive rates is feasible over discrete memoryless classical, classical-quantum, and quantum channels. For classical point-to-point channels, we show that if the dimension of the channel input probability simplex exceeds that of the channel output probability simplex, equivalently, if the input alphabet has larger cardinality than the output alphabet, then positive covert rates are achievable for certain classes of Discrete Memoryless Channels (DMCs). We further show that allowing the innocent symbol (i.e., the symbol transmitted in the no-communication mode) to be chosen appropriately can enlarge the class of DMCs for which positive covert rates are achievable. We also study covert communication over classical Multiple-Access Channels (MACs), where the additional transmitter effectively enlarges the set of available channel input pairs, and we show that the conditions required to satisfy the covertness constraint are less restrictive for MACs than for point-to-point channels. We extend these results to classical-quantum DMCs by showing that if the dimension of the input probability simplex exceeds the affine dimension of the set of output states that can be induced at the channel output, then positive covert rates are achievable for certain classes of classical-quantum DMCs. Finally, for quantum channels, we show that if the innocent state (i.e., the state transmitted in the no-communication mode) is mixed, then the covertness constraint can always be satisfied by a non-trivial input ensemble. Consequently, positive covert rates are achievable whenever the legitimate receiver can distinguish at least two states in a suitable such ensemble.

Problem

• covert communication
• discrete memoryless channels
• classical-quantum channels
• quantum channels
• positive covert rates

Innovation

• Covert Communication
• Quantum Channels
• Classical-Quantum Channels
• Discrete Memoryless Channels
• Positive Covert Rates