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arXiv:2609.36162

From Classical to Quantum Channels: Achieving Positive Covert Rates

Hassan ZivariFard, Xiaodong Wang, Alexei Ashikhmin

quant-phcs.ITSubmitted Sep 28, 2026• Announced Sep 30, 2026• 0 citations
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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.

Comments
44 pages, 9 figures, single column, part of the results will be presented at the 2026 IEEE Information Theory Workshop

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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.
We study covert classical communication over quantum multiple-access channels (MACs) with general message sets. Specifically, we consider a fully quantum MAC with arbitrary message sets and an arbitrary number of transmitters. We demonstrate the feasibility of achieving a positive covert rate over this channel and establish general one-shot and asymptotic achievable rate regions. For classical-quantum MACs with general message sets, we establish the covert capacity, when the transmitters are restricted to deterministic encoding. Our result recovers, as a special case, known results for classical communication over classical MACs with general message sets, covert communication of a classical message over a classical channel with two transmitters, and classical communication over quantum MACs. We provide three examples of MACs to which our results can be applied, either directly or indirectly, to achieve positive covert rates. Specifically, we first study covert communication over a finite-dimensional MAC with a helper. We then analyze a classical Gaussian MAC with a helper and derive its covert capacity. Finally, we extend the analysis to a single-mode bosonic MAC with a helper and show that positive covert rates can also be achieved in this setting. To the best of our knowledge, this is the first work to achieve positive-rate covert communication over both classical and quantum MACs.
This paper characterizes the covert capacity-key tradeoffs for discrete memoryless channels (DMC) and discrete memoryless multiple-access channels (DMMAC). The focus is on channels where communication rates are measured as the number of transmitted bits divided by the square-root of the blocklength and by the square-root of the covertness constraint. Previous results had determined the largest achievable covert rates for these channels, as well as the minimum key rates required to achieve these largest covert rates. In this work, we additionally determine the minimum key rates required at reduced covert rates. Stated differently, we determine the set of all covert rates that are achievable for a given set of key rates. This is termed thecovert capacity-key tradeoff. Our results on the covert capacity-key tradeoffs over DMCs and DMMACs show that for small key rates and when the adversary observes the inputs through a better channel than the legitimate receiver, binary signalling at all transmitters is optimal even for larger input alphabets and the capacity-key tradeoff grows linearly. Moreover, in this regime the covert capacity-key tradeoff of DMMACs is square implying that each of the transmitters can simultaneously achieve its own largest covert rate depending only on its own available key rate, irrespective of the other transmitter. For larger key rates or when the adversary is not uniformly stronger than the legitimate receiver over all inputs, the covert capacity-key tradeoff region of DMMACs is non-square and a tradeoff arises between the rates of the various transmitters.
This paper explores the tradeoff between covert communication capacity and secret key requirements over discrete memoryless channels (DMCs). We focus on settings where under a covertness constraint both communication and key rates are measured as the number of bits per square root of the block-length. While previous work has identified the maximum covert communication rates and the corresponding minimum key rates needed to achieve them, our study characterizes the minimum key rates necessary for all of desired covert communication rates. In equivalent terms, we determine, for any given key rate, the set of achievable covert rates. This relationship defines what we call the covert capacity-key tradeoff.Our analysis reveals several new insights. In scenarios where only small key rates are available and the adversary has a stronger channel than the intended receiver, binary signaling is optimal—regardless of the specific channel characteristics or input alphabets. In these cases, the covert capacity increases linearly with the available key rate. In other cases and for larger key rates, the covert capacity-key tradeoff grows sublinearly.We also extend our findings to multi-access channels (MACs) with binary inputs.
We study covert classical communication over a quantum multiple-access channel (MAC) with a helper. Specifically, we consider three transmitters, where one transmitter helps the other two transmitters communicate covertly with a receiver. We demonstrate the feasibility of achieving a positive covert rate over this channel and establish an achievable rate region. Our result recovers as a special case known results for classical communication over classical MACs with a degraded message set, classical communication over quantum MACs, and classical communication over MACs with a helper. To the best of our knowledge, our result is the first to achieve covert communication with positive rates over both classical and quantum MACs.
This paper studies covert communication over channels with Action-Dependent State Information (ADSI) when the state is available either non-causally or causally at the transmitter. Covert communication refers to reliable communication between a transmitter and a receiver while ensuring a low probability of detection by an adversary, which we refer to as “warden”. It is well known that in a point-to-point Discrete Memoryless Channel (DMC), it is possible to communicate on the order ofN\sqrt {N}N​bits reliably and covertly over N channel uses while the transmitter and the receiver are required to share a secret key on the order ofN\sqrt {N}N​bits. This paper studies achieving reliable and covert communication of positive rate, i.e., reliable and covert communication on the order of N bits in N channel uses, over a channel with ADSI while the transmitter has non-causal or causal access to the ADSI, and the transmitter and the receiver share a secret key of negligible rate. We derive achievable rates for both the non-causal and causal scenarios by using block-Markov encoding and secret key generation from the ADSI, which subsumes the best achievable rates for channels with random states. We also derive upper bounds, for both non-causal and causal scenarios, that meet our achievable rates for some special cases. As an application of our problem setup, we study covert communication over channels with rewrite options, which are closely related to recording covert information on memory, and show that a positive covert rate can be achieved in such channels. As a special case of our problem, we study the Additive White Gaussian Noise (AWGN) channels and provide lower and upper bounds on the covert capacity that meet when the transmitter and the receiver share a secret key of sufficient rate and when the warden’s channel is noisier than the legitimate receiver channel. As another application of our problem setup, we show that cooperation can lead to a positive covert rate in Gaussian channels. A few other examples are also worked out in detail.
We study covert communication and covert secret key generation with positive rates over quantum state-dependent channels. Specifically, we consider fully quantum state-dependent channels when the transmitter shares an entangled state with the channel. We study this problem setting under two security metrics. For the first security metric, the transmitter aims to communicate covertly with the receiver while simultaneously generating a covert secret key, and for the second security metric, the transmitter aims to transmit a secure message covertly and generate a covert secret key with the receiver simultaneously. Our main results include one-shot and asymptotic achievable positive covert-secret key rate pairs for both security metrics. Our results recover as a special case the best-known results for covert communication over state-dependent classical channels. To the best of our knowledge, our results are the first instance of achieving a positive rate for covert secret key generation and the first instance of achieving a positive covert rate over a quantum channel. Additionally, we show that our results are optimal when the channel is classical and the state is available non-causally at both the transmitter and the receiver.