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arXiv:2105.14505 · Physical Review Applied

Computation-Aided Classical-Quantum Multiple Access to Boost Network Communication Speeds

Masahito Hayashi, M. A. Vázquez‐Castro

Published Nov 10, 2021• 18 citations
arXivHTMLPDF

Abstract

A multiple access channel (MAC) consists of multiple senders simultaneously transmitting their messages to a single receiver. For the classical-quantum case (CQ MAC), achievable rates are known assuming that all the messages are decoded, a common assumption in quantum network design. However, such a conventional design approach ignores the global network structure, i.e., the network topology. When a CQ MAC is given as a part of quantum network communication, this work shows that computation properties can be used to boost communication speeds with code design dependent on the network topology. We quantify achievable quantum communication rates of codes with the computation property for a two-sender CQ MAC. When the two-sender CQ MAC is a boson coherent channel with binary discrete modulation, we show that it achieves the maximum possible communication rate (the single-user capacity), which cannot be achieved with conventional design. Further, such a rate can be achieved by different detection methods: quantum (with and without quantum memory), on-off photon counting, and homodyne (each at different photon power). Finally, we describe two practical applications, one of which cryptographic.

DOI
10.1103/physrevapplied.16.054021

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A multiple access channel (MAC) consists of multiple senders simultaneously transmitting their messages to a single receiver. For the classical-quantum case (CQ MAC), achievable rates are known assuming that all the messages are decoded, a common assumption in quantum network design. However, such a conventional design approach ignores the global network structure, i.e., the network topology. When a CQ MAC is given as a part of quantum network communication, this work shows that computation properties can be used to boost communication speeds with code design dependent on the network topology. We quantify achievable quantum communication rates of codes with the computation property for a two-sender CQ MAC. When the two-sender CQ MAC is a boson coherent channel with binary discrete modulation, we show that it achieves the maximum possible communication rate (the single-user capacity), which cannot be achieved with conventional design. Further, such a rate can be achieved by different detection methods: quantum (with and without quantum memory), on-off photon counting, and homodyne (each at different photon power). Finally, we describe two practical applications, one of which cryptographic.
Communication networks have multiple users, each sending and receiving messages. A multiple access channel (MAC) models multiple senders transmitting to a single receiver, such as the uplink from many mobile phones to a single base station. The optimal performance of a MAC is quantified by a capacity region of simultaneously achievable communication rates. We study the two-sender classical MAC, the simplest and best-understood network, and find a surprising richness in both a classical and quantum context. First, we find that quantum entanglement shared between senders can substantially boost the capacity of a classical MAC. Second, we find that optimal performance of a MAC with bounded-size inputs may require unbounded amounts of entanglement. Third, determining whether a perfect communication rate is achievable using finite-dimensional entanglement is undecidable. Finally, we show that evaluating the capacity region of a two-sender classical MAC is in fact NP-hard.
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.
Extension of point-to-point communication model to the realm of multi-node configurations finds a plethora of applications in internet and telecommunication networks. Here, we establish a novel advantage of quantum communication in a commonly encountered network configuration known as the Multiple Access Channel (MAC). A MAC consists of multiple distant senders aiming to send their respective messages to a common receiver. Unlike the quantum superdense coding protocol, the advantage reported here is realized without invoking entanglement between the senders and the receiver. Notably, such an advantage is unattainable in traditional point-to-point communication involving one sender and one receiver, where the limitations imposed by the Holevo and Frankel Weiner no-go theorems come into play. Within the MAC setup, this distinctive advantage materializes through the receiver's unique ability to simultaneously decode the quantum systems received from multiple senders. Intriguingly, some of our MAC designs draw inspiration from various other constructs in quantum foundations, such as the Pusey-Barrett-Rudolph theorem and the concept of `nonlocality without entanglement', originally explored for entirely different purposes. Beyond its immediate applications in network communication, the presented quantum advantage hints at a profound connection with the concept of `quantum nonlocality without inputs' and holds the potential for semi-device-independent certification of entangled measurements.
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.
We investigate a quantum integrated communication and computation (QICC) scheme for a single-mode bosonic multiple-access channel (MAC) with coherent-state signalling. By exploiting the natural superposition property of the quantum MAC, a common receiver simultaneously performs over-the-air computation (OAC) on the analogue symbols transmitted by one set of devices and decodes multiple-access data from another. The joint design of the transmit power control and the receive coefficient leads to a non-convex optimization problem that maximizes computation accuracy under a prescribed sum-rate communication constraint. To address this challenge, we develop a low-complexity alternating-optimization framework that incorporates: (i) closed-form linear minimum-mean square error updates for the receive coefficient, (ii) monotonicity properties of the quantum sum-rate constraint, and (iii) projected-gradient refinements for the communication powers. The proposed QICC scheme achieves an effective computation–communication trade-off with fast convergence and low computational complexity.
We investigate a quantum integrated communication and computation (QICC) scheme for a single-mode bosonic multiple-access channel (MAC) with coherent-state signalling. By exploiting the natural superposition property of the quantum MAC, a common receiver simultaneously performs over-the-air computation (OAC) on the analogue symbols transmitted by one set of devices and decodes multiple-access data from another. The joint design of the transmit power control and the receive coefficient leads to a non-convex optimization problem that maximizes computation accuracy under a prescribed sum-rate communication constraint. To address this challenge, we develop a low-complexity alternating-optimization framework that incorporates: (i) closed-form linear minimum-mean square error updates for the receive coefficient, (ii) monotonicity properties of the quantum sum-rate constraint, and (iii) projected-gradient refinements for the communication powers. The proposed QICC scheme achieves an effective computation-communication trade-off with fast convergence and low computational complexity.