We consider the problem of covert communication over the entanglement-assisted (EA) bosonic multiple access channel (MAC). We derive a closed-form achievable rate region for the general EA bosonic MAC using high-order phase-shift keying (PSK) modulation. Specifically, we demonstrate that in the low-photon regime the capacity region collapses into a rectangle, asymptotically matching the point-to-point capacity as multi-user interference vanishes. We also characterize an achievable covert throughput region, showing that entanglement assistance enables an aggregate throughput scaling of \(O(\sqrt{n} \log n)\) covert bits with the block length $n$ for both senders, surpassing the square-root law as in the point-to-point case. Our analysis reveals that the joint covertness constraint imposes a linear trade-off between the senders throughput.
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35 pages. Full technical version; includes detailed proofs for all main results
We consider the problem of covert communication over the entanglement-assisted (EA) bosonic multiple access channel (MAC). We derive a closed-form achievable rate region for the general EA bosonic MAC using high-order phase-shift keying (PSK) modulation. Specifically, we demonstrate that in the low-photon regime the capacity region collapses into a rectangle, asymptotically matching the point-to-point capacity as multi-user interference vanishes. We also characterize an achievable covert throughput region, showing that entanglement assistance enables an aggregate throughput scaling of (O(\sqrt{n} \log n)) covert bits with the block length n for both senders, surpassing the square-root law as in the point-to-point case. Our analysis reveals that the joint covertness constraint imposes a linear trade-off between the senders throughput.
We solve the entanglement-assisted (EA) classical capacity region of quantum multiple-access channels with an arbitrary number of senders, which is conjectured by Hsieh, Devetak and Winter. As an example, we consider the bosonic thermal-loss multiple-access channel and solve the rate region enabled by an entanglement source composed of sender-receiver pairwise two-mode squeezed vacuum states. The EA rate region is strictly larger than the capacity region without entanglement-assistance, therefore also larger than the Yen-Shapiro rate-region of Gaussian encoding or coherent-state encoding. When the senders have equal low brightness, we also numerically find that the two-mode squeezed vacuum source is optimal at a corner rate point. With two-mode squeezed vacuum states as the source and phase modulation as the encoding, we also design practical receiver protocols to realize the entanglement advantages. In the parameter region of a large noise background, the receivers can enable a simultaneous rate advantage of 82.0% for each sender with binary phase-shift keying. Due to teleportation and superdense coding, our results for EA classical communication can be directly extended to EA quantum communication at half of the rates.
Abstract We solve the entanglement-assisted (EA) classical capacity region of quantum multiple-access channels (MACs) with an arbitrary number of senders. As an example, we consider the bosonic thermal-loss MAC and solve the one-shot capacity region enabled by an entanglement source composed of sender-receiver pairwise two-mode squeezed vacuum states. The EA capacity region is strictly larger than the capacity region without entanglement-assistance. With two-mode squeezed vacuum states as the source and phase modulation as the encoding, we also design practical receiver protocols to realize the entanglement advantages. Four practical receiver designs, based on optical parametric amplifiers, are given and analyzed. In the parameter region of a large noise background, the receivers can enable a simultaneous rate advantage of 82.0% for each sender. Due to teleportation and superdense coding, our results for EA classical communication can be directly extended to EA quantum communication at half of the rates. Our work provides a unique and practical network communication scenario where entanglement can be beneficial.
We study quantum-secure covert-communication over lossy thermal-noise bosonic channels, the quantum mechanical model for many practical channels. We derive the expressions for the covert capacity of these channels: Lno-EA, when Alice and Bob share only a classical secret, and LEA, when they benefit from entanglement assistance. Entanglement assistance alters the fundamental scaling law for covert communication. Instead of Lno-EA√n-rno-EA(n), rno-EA(n) = o(√n), entanglement assistance allows LEA√n log n - rEA(n), rEA(n) = o(√n log n), covert bits to be transmitted reliably over n channel uses. However, noise in entanglement storage erases the log n gain from our achievability; work on the matching converse is ongoing.
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.
We establish the fundamental limits of covert communication over quantum channels, focusing on both finite-dimensional classical-quantum (CQ) channels and the infinite-dimen\-sional lossy thermal-noise bosonic channel. For general memoryless CQ channels, we characterize when covert communication is possible and prove a square root law (SRL): at most Ln+o(n) bits can be reliably transmitted covertly over n uses of the channel where L is the channel-dependent covert capacity. We derive a single-letter expression for L and show that the required pre-shared secret key also scales as n under mild conditions. We also identify and characterize corner cases where either constant-rate or zero-rate covert communication is possible. For the bosonic channel, we prove that the SRL holds and derive exact covert capacities under different resource assumptions. In particular, we show that the covert secrecy and covert entanglement generation capacities both equal the covert classical capacity without entanglement-assistance, Lno-EA, and show that the required pre-shared classical secret key scales as n. We also find that quadrature phase-shift keying (QPSK) achieves the optimal covert capacity, outperforming binary modulation in contrast to the classical channel setting. When Alice and Bob instead share entanglement, the covert classical capacity improves to LEAnlogn+o(nlogn), though this scaling is sensitive to noise in the entangled resource. Finally, we propose a practical covert transceiver and simulate its performance compared to recently experimentally-tested transceivers under realistic conditions.
Entanglement is a valuable quantum resource in quantum information processing. In classical communication over quantum channels, it is known to boost the communication rate drastically. To generalize such a boost to more general scenarios, we provide computable limits on the communication over optical multiple-access channels (MACs) for both the entanglement-assisted and unassisted communication. For the unassisted case, we generalize the coherent-state achievable rate region and outer bound known for the thermal-loss case [B. J. Yen and J. H. Shapiro, Phys. Rev. A 72, 062312 (2005)] to general bosonic Gaussian MACs. For the assisted case, we generalize the two-mode squeezed vacuum rate region and the outer bound for the thermal-loss case [H. Shi et al., npj Quantum Inf. 7, 74 (2021)] to general bosonic MACs. In terms of the total communication rate of all senders, we prove additivity for general MACs, generalizing the two-sender version in M.-H. Hsieh et al., IEEE Trans. Inf. Theory 54, 3078 (2008). Furthermore, for optical communication modeled as phase-insensitive bosonic Gaussian MACs, we prove that the optimal total rate is achieved by Gaussian entanglement and therefore can be efficiently evaluated. The computable limits confirm entanglement's boosts in optical multiple-access communications. Finally, we formulate an entanglement-assisted version of minimum entropy conjecture, which leads to the additivity of the capacity region of phase-insensitive bosonic Gaussian MACs if it is true.