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arXiv:2506.17803 · IEEE Transactions on Information Theory

Virtual Signaling of CSIT via Non-Signaling Assistance

Yuhang Yao, Syed A. Jafar

Published Aug 10, 2026• 0 citations

Abstract

Non-signaling correlations, which (strictly) include quantum correlations, provide a tractable path to explore the potential impact of quantum nonlocality on the capacity of classical communication networks. Motivated by a recent discovery that certain wireless network settings benefit significantly from non-signaling (NS) correlations, various generalizations are considered. First, it is shown that for a point to point discrete memoryless channel with a non-causal channel state information at the transmitter (CSIT), the NS-assisted Shannon capacity matches the classical (without NS assistance) capacity of the channel for the setting where the state is also made available to the receiver. The key insight is summarized as 'virtual signaling of CSIT via NS-assistance' and is supported by further results as follows. For a discrete memoryless 2-user broadcast channel (BC), the Shannon capacity region with NS-assistance available only between the transmitter and User 1, is found next. Consistent with the aforementioned key insight, the result matches the classical capacity region for the setting where the desired message of User 2 is made available in advance as side-information to User 1. The latter capacity region is known from a result of Kramer and Shamai. Next, for a semi-deterministic BC, the Shannon capacity region with full (tripartite) NS-assistance is shown to be the same as if only bipartite NS-assistance was available between the transmitter and the non-deterministic user. Bipartite NS-assistance between the transmitter and only the deterministic user, does not improve the capacity region relative to the corresponding classical setting. Finally, the analysis is extended to a K-user BC with full NS-assistance among all parties.

DOI: 10.1109/tit.2026.3722092

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Non-signaling correlations, which (strictly) include quantum correlations, provide a tractable path to explore the potential impact of quantum nonlocality on the capacity of classical communication networks. Motivated by a recent discovery that certain wireless network settings benefit significantly from non-signaling (NS) correlations, various generalizations are considered. First, it is shown that for a point to point discrete memoryless channel with a non-causal channel state information at the transmitter (CSIT), the NS-assisted Shannon capacity matches the classical (without NS assistance) capacity of the channel for the setting where the state is also made available to the receiver. The key insight is summarized as 'virtual signaling of CSIT via NS-assistance' and is supported by further results as follows. For a discrete memoryless 2-user broadcast channel (BC), the Shannon capacity region with NS-assistance available only between the transmitter and User 1, is found next. Consistent with the aforementioned key insight, the result matches the classical capacity region for the setting where the desired message of User 2 is made available in advance as side-information to User 1. The latter capacity region is known from a result of Kramer and Shamai. Next, for a semi-deterministic BC, the Shannon capacity region with full (tripartite) NS-assistance is shown to be the same as if only bipartite NS-assistance was available between the transmitter and the non-deterministic user. Bipartite NS-assistance between the transmitter and only the deterministic user, does not improve the capacity region relative to the corresponding classical setting. Finally, the analysis is extended to a K-user BC with full NS-assistance among all parties.

The non-signaling (NS) assisted capacity of a classical discrete memoryless channel with causal channel state information at the transmitter (CSIT) is shown to be

C^{NS,ca}=\max_{P_{X|S}}I(X;Y\mid S)

, where

X, Y, S

correspond to the input, output and state of the channel. Remarkably, this is the same as the capacity of the channel in the NS-assisted non-causal CSIT setting,

C^{NS,nc}=\max_{P_{X|S}}I(X;Y\mid S)

, which was previously established, and also matches the (either classical or with NS assistance) capacity of the channel where the state is available not only (either causally or non-causally) to the transmitter but also to the receiver. While the capacity remains unchanged, the optimal probability of error for fixed message size and blocklength, in the NS-assisted causal CSIT setting can be further improved if channel state is made available to the receiver. This is in contrast to corresponding NS-assisted non-causal CSIT setting where it was previously noted that the optimal probability of error cannot be further improved by providing the state to the receiver. As a separate result we prove that non-signaling assistance, feedback, and strictly causal CSIT (i.e., transmitter knows only past channel states but not the current or future states), each of which is individually already known to not increase capacity, also cannot increase capacity when they are collectively made available to the transmitter.

The capacity region of the

K

-user discrete memoryless broadcast channel is fully characterized when non-signaling (NS) assistance is available to the transmitter and all

K

receivers. The NS-assisted capacity region is shown to coincide with Sato's region, i.e., the region defined by sum-rate bounds over all subsets of messages, where each bound corresponds to full cooperation among that subset of receivers under a worst-case joint channel law consistent with the marginal channels.

The capacity region of the

K

-sender discrete memoryless multiple access channel (MAC) is fully characterized when non-signaling (NS) assistance is available to all

K

transmitters and the receiver. It is shown to have the same form as the classical capacity region of the MAC, except that the input distribution is allowed to be arbitrarily dependent across the senders. In particular, the NS-assisted capacity region matches the natural generalization to

K

senders of an outer bound that was previously established by Fawzi and Fermé for

K=2

senders. Additionally, we provide examples of

K

-sender MACs where the multiplicative gain in capacity from NS-assistance is arbitrarily close to

K

. Combined with an upper bound from prior work, this establishes

K

as the extremal value of the multiplicative gain from NS-assistance across all

K

-sender MAC settings.

Quantum entanglement assistance is known to improve the Shannon capacity of classical communication networks but the largest gains noted thus far are rather modest (less than 6%), motivating the question: are large capacity gains ever possible? It is shown in this work that in the presence of causal channel state information at the transmitters (CSIT), quantum entanglement assistance provides a multiplicative capacity advantage that grows exponentially with the number of users K for certain classical K-user multiple access channels with fixed size (binary) alphabet for inputs, outputs and states. Similarly, in the presence of causal channel state information at the transmitters, quantum entanglement assistance is shown to provide a multiplicative capacity advantage that is unbounded as the size of the state alphabet grows, while the number of users (K=3) and the input and output alphabet (binary) are held fixed. Even with only a few users and small alphabet sizes, substantial multiplicative gains in capacity are found, e.g., with binary inputs, outputs and states, multiplicative gains by factors exceeding 21 and 88 are noted with K=5 and K=7 users, respectively. The gains are robust in the sense that they persist even with noisy quantum resources, e.g., an exponential (in K) capacity advantage from quantum entanglement assistance remains available even if each entangled qubit independently depolarizes completely with probability

\approx

30%. The gains are based on quantum entanglement assistance provided only to the transmitters.

Extracting the full power of non-local correlations in prepare-and-measure (PM) scenarios requires precise control over the timing and structure of the receiver's measurements. Indeed, recent developments in entanglement-assisted classical communication scenarios have shown that adaptive strategies-where the receiver uses the transmitted message to guide their measurement choice-can outperform standard non-adaptive protocols. Moving beyond quantum theory, however, the ultimate limits of such advantages remain largely unexplored. In this work, we thoroughly study adaptive and non-adaptive non-signaling (NS) assistance in PM scenarios with classical communication. We provide simple characterizations of the sets of behaviors that can be realized using both non-adaptive and adaptive NS assistance in arbitrary PM scenarios. As a consequence, we show that non-adaptive NS assistance is already strong enough to reproduce quantum communication with the same message dimension: the transmission of a qudit can be simulated by a classical dit assisted non-adaptively by NS correlations. We then compare adaptive and non-adaptive NS assistance. We prove that any adaptive NS advantage can be traced back to scenarios in which the receiver has no measurement choice, ruling out the genuinely multi-setting advantages found in entanglement-assisted quantum protocols. Finally, we identify all PM scenarios where adaptive NS strategies provide a strict advantage over non-adaptive ones.

For classical point-to-point channels, it has been shown by Bennett et al. that quantum entanglement assistance cannot improve their capacity, and by Cubitt et al. that entanglement assistance cannot activate (increase from zero to non-zero) their zero-error capacity. In contrast, we show that for classical point-to-point channels with causal CSIT (channel state information at the transmitter), quantum entanglement assistance can in some cases improve their capacity, and in some cases activate their zero-error capacity.