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The Multiple-Access Channel with Entangled Transmitters

Uzi Pereg, Christian Deppe, Holger Boche

Published Dec 4, 2023• 9 citations
Publisher

Abstract

Communication over a classical multiple-access channel (MAC) with quantum entanglement resources is considered, whereby two transmitters share entanglement resources a priori. Leditzky et al. (2020) presented an example, defined in terms of a pseudo telepathy game, such that the sum rate with entangled transmitters is strictly higher than the best achievable sum rate without such resources. Here, we establish inner and outer bounds on the capacity region for the general MAC with entangled transmitters, and show that the previous result can be obtained as a special case. It has long been known that the capacity region of the classical MAC under a message-average error criterion can be strictly larger than with a maximal error criterion (Dueck, 1978). We observe that given entanglement resources, the regions coincide.

DOI
10.1109/globecom54140.2023.10437777

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Communication over a classical multiple-access channel (MAC) with quantum entanglement resources is considered, whereby two transmitters share entanglement resources a priori. Leditzky et al. (2020) presented an example, defined in terms of a pseudo telepathy game, such that the sum rate with entangled transmitters is strictly higher than the best achievable sum rate without such resources. Here, we establish inner and outer bounds on the capacity region for the general MAC with entangled transmitters, and show that the previous result can be obtained as a special case. It has long been known that the capacity region of the classical MAC under a message-average error criterion can be strictly larger than with a maximal error criterion (Dueck, 1978). We observe that given entanglement resources, the regions coincide.
Communication over a classical multiple-access channel (MAC) with entanglement resources is considered, whereby two transmitters share entanglement resources a priori before communication begins. Leditzky et al. (2020) presented an example of a classical MAC, defined in terms of a pseudo telepathy game, such that the sum rate with entangled transmitters is strictly higher than the best achievable sum rate without such resources. Here, we establish inner and outer bounds on the capacity region for the general MAC with entangled transmitters, and show that the previous result can be obtained as a special case. It has long been known that the capacity region of the classical MAC under a message-average error criterion can be strictly larger than with a maximal error criterion (Dueck, 1978). We observe that given entanglement resources, the regions coincide. Furthermore, we address the combined setting of entanglement resources and conferencing, where the transmitters can also communicate with each other over rate-limited links. Using superdense coding, entanglement can double the conferencing rate.
We investigate secure communication over a classical multiple-access wiretap channel (MAC-WTC), specifically exploring the benefit of shared entanglement between the transmitters. Under the strict semantic security criterion, we derive an achievable rate region and a regularized expression for the secrecy capacity. We further establish a single-letter upper bound on the secure capacity of the MAC-WTC with entangled transmitters. Our results demonstrate that entanglement strictly enlarges the secrecy capacity of MAC-WTC compared to sharing only classical correlated randomness, a finding we illustrate using a pseudo-telepathy game example. Finally, we establish new strong soft-covering lemmas for the output statistics of multipleaccess channels (MACs) with entangled transmitters. Our results generalize existing results for non-entangled systems.
Communication over a classical multiple-access channel (MAC) with entanglement resources is considered, whereby two transmitters share entanglement resources a priori before communication begins. Leditzky et al. (2020) presented an example of a classical MAC, defined in terms of a pseudo telepathy game, such that the sum rate with entangled transmitters is strictly higher than the best achievable sum rate without such resources. Here, we establish inner and outer bounds on the capacity region for the general MAC with entangled transmitters, and show that the previous result can be obtained as a special case. It has long been known that the capacity region of the classical MAC under a message-average error criterion can be strictly larger than with a maximal error criterion (Dueck, 1978). We observe that given entanglement resources, the regions coincide. Furthermore, we address the combined setting of entanglement resources and conferencing, where the transmitters can also communicate with each other over rate-limited links. Using superdense coding, entanglement can double the conferencing rate.
Communication over a multiple-access channel (MAC) with entanglement assisted and conferencing transmitters is considered, where the transmitters can also communicate with each other over rate-limited links. We fully characterize the capacity region for the MAC with entangled transmitters and classical conferencing. We also introduce a quantum conferencing protocol. For the MAC with entangled transmitters and quantum conferencing, we determine a achievable region. This region is generally larger than the capacity region for the MAC with entangled transmitters and classical conferencing. Using superdense coding, entanglement can double the conferencing rate. We continue to discuss potential applications of cooperation between the transmitters for the future 6G system. This is only a short abstract. The long version with all proofs can be found on arxiv [l ],
Communication over a quantum multiple-access channel (MAC) with cribbing encoders is considered, whereby Transmitter 2 performs a measurement on a system that is entangled with Transmitter 1. Based on the no-cloning theorem, perfect cribbing is impossible. This leads to the introduction of a MAC model with noisy cribbing. In the causal and non-causal cribbing scenarios, Transmitter 2 performs the measurement before the input of Transmitter 1 is sent through the channel. Hence, Transmitter 2’s cribbing may inflict a “state collapse” for Transmitter 1. Achievable regions are derived for each setting. Furthermore, a regularized capacity characterization is established for robust cribbing,i.e.when the cribbing system contains all the information of the channel input. Building on the analogy between the noisy cribbing model and the relay channel, a partial decode-forward region is derived for a quantum MAC with non-robust cribbing. For the classical-quantum MAC with cribbing encoders, the capacity region is determined with perfect cribbing of the classical input, and a cutset region is derived for noisy cribbing. In the special case of a classical-quantum MAC with a deterministic cribbing channel, the inner and outer bounds coincide.
Communication over a quantum multiple-access channel (MAC) with cribbing encoders is considered, whereby Transmitter 2 performs a measurement on a system that is entangled with Transmitter 1. Based on the no-cloning theorem, perfect cribbing is impossible. This leads to the introduction of a MAC model with noisy cribbing. In the causal and non-causal cribbing scenarios, Transmitter 2 performs the measurement before the input of Transmitter 1 is sent through the channel. Hence, Transmitter 2's cribbing may inflict a "state collapse" for Transmitter 1. Achievable regions are derived for each setting. Furthermore, a regularized capacity characterization is established for robust cribbing, i.e. when the cribbing system contains all the information of the channel input. Building on the analogy between the noisy cribbing model and the relay channel, a partial decode-forward region is derived for a quantum MAC with non-robust cribbing. For the classical-quantum MAC with cribbing encoders, the capacity region is determined with perfect cribbing of the classical input, and a cutset region is derived for noisy cribbing. In the special case of a classical-quantum MAC with a deterministic cribbing channel, the inner and outer bounds coincide.