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arXiv:2603.20416

Quantum Entanglement Assistance Improves the Capacity and Activates the Zero-Error Capacity of Classical Channels with Causal CSIT

Yuhang Yao, Syed A. Jafar

quant-phcs.ITSubmitted Mar 20, 2026• Announced Mar 24, 2026• 0 citations
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Abstract

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.

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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.
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.
In this paper, we explicitly evaluate the one-shot quantum nonsignaling-assisted zero-error classical capacities M0QNS{\mathcal{M}}_{0}^{\mathrm{QNS}}M0QNS​ for qubit channels. In particular, we show that for nonunital qubit channels M0QNS=0{\mathcal{M}}_{0}^{\mathrm{QNS}}=0M0QNS​=0, which implies that in the one-shot setting nonunital qubit channels cannot transmit any information with zero probability of error even when assisted by quantum nonsignaling correlations. Furthermore, we show that for qubit channels M0QNS{\mathcal{M}}_{0}^{\mathrm{QNS}}M0QNS​ equals the one-shot entanglement-assisted zero-error classical capacity. This means that for a single use of a qubit channel quantum nonsignaling correlations are not more powerful than shared entanglement.
Entanglement-assisted communication over a random-parameter quantum channel with either causal or non-causal channel side information (CSI) at the encoder is considered.This describes a scenario where the quantum channel depends on the quantum state of the input environment.While Bob, the decoder, has no access to this state, Alice, the transmitter, performs a sequence of projective measurements on her environment to encode her message.Dupuis [10,9] established the entanglement-assisted capacity with non-causal CSI.Here, we establish characterization in the causal setting, and also give an alternative proof technique and further observations for the non-causal setting.
Entanglement-assisted communication over a random-parameter quantum channel with either causal or non-causal channel side information (CSI) at the encoder is considered. This describes a scenario where the quantum channel depends on the quantum state of the input environment. While Bob, the decoder, has no access to this state, Alice, the transmitter, performs a sequence of projective measurements on her environment and encodes her message accordingly. Dupuis established the entanglement-assisted capacity with non-causal CSI. Here, we establish characterization in the causal setting, and also give an alternative proof technique and further observations for the non-causal setting.
Quantum Lovász number is a quantum generalization of the Lovász number in graph theory. It is the best known efficiently computable upper bound of the entanglement-assisted zero-error classical capacity of a quantum channel. However, it remains an intriguing open problem whether quantum entanglement can always enhance the zero-error capacity to achieve the quantum Lovász number. In this paper, by constructing a particular class of qutrit-to-qutrit channels, we show that there exists a strict gap between the entanglement-assisted zero-error capacity and the quantum Lovász number. Interestingly, for this class of quantum channels, the quantum generalization of fractional packing number is strictly larger than the zero-error capacity assisted with feedback or no-signaling correlations, which differs from the case of classical channels.
The zero-error capacity of a noisy classical channel quantifies its ability to transmit information with absolute certainty, i.e., without any error. Unlike Shannon's standard channel capacity, which remains unaffected by pre-shared correlations, zero-error capacity can be enhanced through nonlocal correlations. In this work, we investigate zero-error communication utility of such correlations arising in the 2-2-m Bell scenario, where two parties have two inputs and m possible outcomes per input. For all m\geq2, we construct examples of noisy classical channels with zero zero-error capacity that, when assisted by extremal 2-2-m nonlocal correlations, can transmit one bit of information. While nonlocal correlations arising from quantum entangled states cannot achieve a positive zero-error capacity for these channels, they significantly enhance the probability of successfully transmitting a classical bit in a single use. Extending this analysis to the 2-m-2 Bell scenario, we identify channels with zero zero-error capacity that can nonetheless perfectly transmit log m bits of information when assisted by corresponding extremal nonlocal correlations. Our findings underscore the versatile utility of Bell nonlocal correlations in achieving zero-error communication.