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Iranian Conference on Electrical Engineering

Entanglement-Assisted Classical-Quantum Multiple Access Wiretap Channel: One-shot Achievable Rate Region

Hadi Aghaee, Bahareh Akhbari

Published May 17, 2022• 1 citation
Publisher

Abstract

In this paper, the problem of secure communication over an entanglement-assisted classical-quantum multiple access channel is studied under one-shot setting. The main employed approach to this end, is combination of simultaneous decoding and position-based decoding techniques while a recently introduced approach is used to calculate leaked information.

DOI
10.1109/icee55646.2022.9827277

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In this paper, the problem of secure communication over an entanglement-assisted classical-quantum multiple access channel is studied under one-shot setting. The main employed approach to this end, is combination of simultaneous decoding and position-based decoding techniques while a recently introduced approach is used to calculate leaked information.
In this paper, the problem of private communication of classical messages over a quantum multiple access channel under one-shot setting is studied. In this regard, we first introduce general quantum multiple access wiretap channel, and then we calculate an achievable secrecy rate region for the main channel. The encoding process follows the combination of the superposition and Wyner wiretap coding schemes, and the decoding technique is based on the simultaneous decoder and convex splitting. At last, we extend the results to the l-user case.
In this paper, we want to investigate classical-quantum multiple access wiretap channels (CQ-MA-WTC) under one-shot setting. In this regard, we analyze the CQ-MA-WTC using simultaneous position-based decoder for reliable decoding and using a newly introduced technique in order to decode securely. Also, for the sake of comparison, we analyze the CQ-MA-WTC using Sen's one-shot joint typicality lemma for reliable decoding. The simultaneous position-based decoder tends to a multiple hypothesis testing problem. Also, using convex splitting to analyze the privacy criteria in a simultaneous scenario becomes problematic. To overcome both problems, we first introduce a new channel that can be considered as a dual to the CQ-MA-WTC. This channel is called a point-to-point quantum wiretap channel with multiple messages (PP-QWTC). In the following, as a strategy to solve the problem, we also investigate and analyze quantum broadcast channels (QBCs) under the one-shot setting.
We study classical communication over quantum multiple-access channels and their wiretap counterparts with unreliable entanglement assistance. Using a robust superposition coding scheme, we characterize the trade-off between baseline rates that are guaranteed without entanglement and additional rates achievable when entanglement is available. We establish a regularized characterization of the classical capacity region for the quantum multiple-access channel and extend it to regularized secrecy capacity regions under two models: entanglement loss and interception. Specifically, for the class of entanglement-breaking channels, we demonstrate that these regularized regions reduce to computable single-letter formulas.
In this work, we prove a novel one-shot multi-sender decoupling theorem generalising Dupuis result. We start off with a multipartite quantum state, say on A1 A2 R, where A1, A2 are treated as the two sender systems and R is the reference system. We apply independent Haar random unitaries in tensor product on A1 and A2 and then send the resulting systems through a quantum channel. We want the channel output B to be almost in tensor with the untouched reference R. Our main result shows that this is indeed the case if suitable entropic conditions are met. An immediate application of our main result is to obtain a one-shot simultaneous decoder for sending quantum information over a k-sender entanglement unassisted quantum multiple access channel (QMAC). The rate region achieved by this decoder is the natural one-shot quantum analogue of the pentagonal classical rate region. Assuming a simultaneous smoothing conjecture, this one-shot rate region approaches the optimal rate region of Yard, Dein the asymptotic iid limit. Our work is the first one to obtain a non-trivial simultaneous decoder for the QMAC with limited entanglement assistance in both one-shot and asymptotic iid settings; previous works used unlimited entanglement assistance.
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.