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IEEE Transactions on Information Theory

Single-Serving Quantum Broadcast Channel With Common, Individualized, and Confidential Messages

Farzin Salek, Min-Hsiu Hsieh, J.R. Fonollosa

Published Jul 30, 2020• 5 citations
Publisher

Abstract

The two-receiver broadcast channel with primary and third party receivers is studied. The sender wishes to reliably communicate a common (or public) message to both receivers as well as individualized and confidential messages to the primary receiver only. The third party receiver must be kept completely ignorant of the confidential message but there are no secrecy requirements associated to the individualized message. A trade-off arises between the rates of the three messages: when one of the rates is high, the other rates may need to back off to guarantee the reliable transmission of all three messages. In addition, the confidentiality requirement implies availability of local randomness at the transmitter in order to implement a stochastic encoding. This article studies the trade-off between the rates of the common, individualized and confidential messages as well as that of the local randomness in the one-shot regime of a quantum broadcast channel. We provide an achievability region, by proving a conditional version of the convex-split lemma combined with the position-based decoding, as well as a (weak) converse region. We study the asymptotic behaviour of our bounds and recover several well-known asymptotic results in the literature, including simultaneous transmission of classical and quantum information.

DOI
10.1109/tit.2020.3013098

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The two-receiver broadcast channel with primary and third party receivers is studied. The sender wishes to reliably communicate a common (or public) message to both receivers as well as individualized and confidential messages to the primary receiver only. The third party receiver must be kept completely ignorant of the confidential message but there are no secrecy requirements associated to the individualized message. A trade-off arises between the rates of the three messages: when one of the rates is high, the other rates may need to back off to guarantee the reliable transmission of all three messages. In addition, the confidentiality requirement implies availability of local randomness at the transmitter in order to implement a stochastic encoding. This article studies the trade-off between the rates of the common, individualized and confidential messages as well as that of the local randomness in the one-shot regime of a quantum broadcast channel. We provide an achievability region, by proving a conditional version of the convex-split lemma combined with the position-based decoding, as well as a (weak) converse region. We study the asymptotic behaviour of our bounds and recover several well-known asymptotic results in the literature, including simultaneous transmission of classical and quantum information.
The 2-receiver broadcast channel with primary and third-party receivers is studied. The messages are classified into public, private and confidential. The messages in the public class are messages intended for both receivers. The private messages are intended for the primary receiver with no secrecy requirements imposed upon them. And the confidential messages are aimed exclusively to the primary receiver such that they must not be accessible to the other receiver. The encoder performs the necessary encryption by virtue of local randomness whose rate is assumed to be limited. We find an achievability region on the trade-off between the rates of the three messages and the source of randomness in the one-shot regime of a quantum broadcast channel.
We study the transmission of two independent confidential classical messages over a quantum broadcast channel, one for each receiver. Each message must remain secret from the other receiver, including when that receiver knows its own message. For classical inputs and quantum outputs, we establish the classical Marton-type inner bound under average reliability and conditional strong secrecy. The encoder selects pairs of codewords from independently generated codebooks using normalized likelihood weights. We prove reliability through a change-of-distribution argument. Our main technical result is a bipartite classical-quantum resolvability theorem that accounts for the dependence created by pair selection and establishes secrecy for the same encoder. We also obtain a multi-letter capacity characterization and extend it to arbitrary quantum inputs under secrecy against the other receiver, together with the Stinespring environment. We recover confidential capacity regions for deterministic classical and degraded classical-quantum channels, with an explicit evaluation for the classical Blackwell channel. For coherent isometric extensions of injective deterministic classical broadcast channels, we show that the confidential classical capacity region equals that of the corresponding classical channel. We then compare confidential classical communication with quantum transmission. For the coherent isometric extension of the Blackwell channel, we determine the unassisted quantum-capacity region and show that some achievable confidential classical rate pairs lie outside it. The Platypus channel provides another example of this separation.
This paper studies the problem of secure communication over the broadcast channel with receiver-side information under the lens of individual secrecy constraints, that is, the transmitter wants to send two independent messages to two receivers, which have, respectively, the desired message of the other receiver as side information, while keeping the eavesdropper ignorant of each message (i.e., the information leakage rate from each message to the eavesdropper is made vanishing). Building upon one-time pad, secrecy coding, and broadcasting schemes, achievable rate regions are investigated, and the capacity region for special cases of either a weak or strong eavesdropper (compared to both legitimate receivers) is characterized. Interestingly, the capacity region for the former corresponds to a line and the latter corresponds to a rectangle with missing corners; a phenomenon occurring due to the coupling between user's rates. Moreover, the individual secrecy capacity region is also fully characterized for the case where the eavesdropper's channel is deterministic. In addition to discrete memoryless setup, Gaussian scenarios are studied. For the Gaussian model, in addition to the strong and weak eavesdropper cases, the capacity region is characterized for the low and high SNR regimes when the eavesdropper's channel is stronger than one receiver but weaker than the other. Remarkably, positive secure transmission rates are always guaranteed under the individual secrecy constraint, unlike the case of the joint secrecy constraint (i.e., the information leakage rate from both messages to the eavesdropper is made vanishing). Thus, this notion of secrecy serves as an appropriate candidate for trading off secrecy level and transmission rate, making secrecy more affordable but still acceptable to the end user.
We study the transmission of a common message and three confidential messages over a broadcast channel with two legitimate receivers and an eavesdropper. Each legitimate receiver is interested in decoding two of the three confidential messages, while having the third one as side information. In order to measure the ignorance of the eavesdropper about the confidential messages, we investigate two different secrecy criteria: joint secrecy and individual secrecy. For both criteria, we provide a general achievable rate region. We establish both the joint and individual secrecy capacity if the two legitimate receivers are less noisy than the eavesdropper. We further investigate the scenario where the eavesdropper is less noisy than the two legitimate receivers. It is known that the joint secrecy constraints can not be fulfilled under this scenario, however, we manage to establish a non vanishing capacity region for the individual secrecy case.
We study the communication capabilities of a quantum channel under the most general channel model known as the one-shot model. Unlike classical channels that can only be used to transmit classical information (bits), a quantum channel can be used for transmission of classical information, quantum information (qubits) and simultaneous transmission of classical and quantum information. In this work, we investigate the one-shot capabilities of a quantum channel for simultaneously transmitting bits and qubits. This problem was studied in the asymptotic regime for a memoryless channel where a regularized characterization of the capacity region was reported. It is known that the transmission of private classical information is closely related to the problem of quantum information transmission. We resort to this idea and find achievable and converse bounds on the simultaneous transmission of the public and private classical information. Then shifting the classical private rate to the quantum information rate leads to a rate region for simultaneous transmission of classical and quantum information. In the case of asymptotic i.i.d. setting, our one-shot result is evaluated to the known results in the literature. Our main tools used in the achievability proofs are position-based decoding and convex-split lemma.
We study secure communication in which two confidential messages are transmitted over a broadcast channel to two legitimate receivers, while keeping an eavesdropper ignorant. Each legitimate receiver is interested in decoding one confidential message, while having the other one as side information. In order to measure the secrecy of the communication, we investigate two different secrecy criteria: joint secrecy and individual secrecy. For both criteria, we provide an achievable rate region and a matching multi-letter outer bound presenting a multi-letter description for the capacity region. We further investigate the class of more capable channels and provide a single-letter converse establishing the secrecy capacity region, not only for more capable channels but less noisy and degraded channels as well. Our results indicate that the secrecy capacity for individual secrecy is higher than the one for joint secrecy, as one message can be used as a secret key for the other one.