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arXiv:2106.13310

Secure communication over generalised quantum multiple access channels

Tamoghna Das, Karol Horodecki, Robert Pisarczyk

Published Jun 24, 2021• 2 citations
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Abstract

We investigate the security of generalized quantum multiple-access channels. We provide the formula for the achievable rate region of secure communication in the scenario of two senders and a single receiver. We explicitly specify a protocol for secure communication in this scenario, which employs superdense coding. The protocol is based on the distribution of a tripartite GHZ state. It allows for both symmetric and asymmetric key distribution whereby one of the senders can have twice the capacity of the other sender. We prove the security of the protocol against general quantum attacks, analyze different strategies of the eavesdropper and compute the key rate for a range of noisy quantum channels.

DOI
10.48550/arxiv.2106.13310

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We investigate the security of generalized quantum multiple-access channels. We provide the formula for the achievable rate region of secure communication in the scenario of two senders and a single receiver. We explicitly specify a protocol for secure communication in this scenario, which employs superdense coding. The protocol is based on the distribution of a tripartite GHZ state. It allows for both symmetric and asymmetric key distribution whereby one of the senders can have twice the capacity of the other sender. We prove the security of the protocol against general quantum attacks, analyze different strategies of the eavesdropper and compute the key rate for a range of noisy quantum channels.
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Abstract Superdense coding uses entanglement as a resource to communicate classical information efficiently through quantum channels. A superdense coding method is optimal when its capacity reaches Holevo bound. We show that for optimality, maximal entanglement is a necessity across the bipartition of Alice and Bob, but neither absolute nor genuine multipartite entanglement is required. Unlike the previous schemes, which can transmit either even or odd bits of information, we demonstrate a generalized dense coding protocol using the genuine multipartite entangled GHZ state to send arbitrary information bits. Expressed in the eigenbasis of different Pauli operators, GHZ state is characterized by a unique parity pattern which enables us to formulate a security checking technique to ensure absolute security of the protocol. We show this method is better applicable in a scenario, where the initial information is distributed among spatially separated parties. Finally, optimizing the number of qubit(s) sent to Bob, we construct a distributed dense coding method, which completely depicts absolutely secure quantum communication between many to one party.
We investigate the maximum rates for transmitting quantum information, distilling entanglement, and distributing secret keys between a sender and a receiver in a multipoint communication scenario, with the assistance of unlimited two-way classical communication involving all parties. First we consider the case where a sender communicates with an arbitrary number of receivers, a so-called quantum broadcast channel. Here we also provide a simple analysis in the bosonic setting where we consider quantum broadcasting through a sequence of beamsplitters. Then, we consider the opposite case where an arbitrary number of senders communicate with a single receiver, a so-called quantum multiple-access channel. Finally, we study the general case of all-in-all quantum communication where an arbitrary number of senders communicate with an arbitrary number of receivers. Since our bounds are formulated for quantum systems of arbitrary dimension, they can be applied to many different physical scenarios involving multipoint quantum communication.
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.
We study private classical communication over quantum multiple-access channels. For an arbitrary number of transmitters, we derive a regularized expression of the capacity region. In the case of degradable channels, we establish a single-letter expression for the best achievable sum-rate and prove that this quantity also corresponds to the best achievable sum-rate for quantum communication over degradable quantum multiple-access channels. Our achievability result decouples the reliability and privacy constraints, which are handled via distributed source coding with quantum side information at the receiver and distributed hashing, respectively. As a by-product of independent interest, we derive a distributed leftover hash lemma against quantum side information that ensures privacy in our achievability result.