Quantum Byzantine Multiple Access Channels

TL;DR

Problem: characterizing reliable communication over a classical-quantum MAC with at most one adversarial transmitter (Byzantine model). Approach: formulate the Byzantine CQ-MAC, show decoding order matters due to quantum state disturbance, and derive a achievable random capacity region for the 2-user case using permutation-based random codes and an effective channel $C_{E_1}$ after decoding the first message. Main findings: for decoding order where sender 1 is decoded first, the achievable region is $R_1 ≤ \max_{p_1} \min_{p_2} I(p_1, B)$ and $R_2 ≤ \max_{p_2} \min_{p_1} I(p_2, E_1 B)$, with extensions to $k≥3$; the work relies on random coding and separable decoding. Significance: advances understanding of security and reliability in quantum networks under internal threats, and identifies key open challenges in applying classical adversarial-sender techniques to quantum arbitrarily varying channels, including the development of new symmetrizability notions.

Abstract

In communication theory, attacks like eavesdropping or jamming are typically assumed to occur at the channel level, while communication parties are expected to follow established protocols. But what happens if one of the parties turns malicious? In this work, we investigate a compelling scenario: a multiple-access channel with two transmitters and one receiver, where one transmitter deviates from the protocol and acts dishonestly. To address this challenge, we introduce the Byzantine multiple-access classical-quantum channel and derive an achievable communication rate for this adversarial setting.

Figures (5)

• Figure 1: classical-quantum 3-user byzantine-multiple access channel, one user may be adversarial.
• Figure 2: Sender $1$ is trustworthy, while sender $2$ is adversarial. The receiver first decodes the message from sender $1$, followed by the message from sender $2$.
• Figure 3: Sender $2$ is trustworthy, while sender $1$ is adversarial. The receiver first decodes the message from sender $1$, followed by the message from sender $2$.
• Figure 4: Sender $2$ is trustworthy, while sender $1$ is adversarial. The receiver first decodes sender $2$'s message, followed by sender $1$'s message.
• Figure 5: Sender $1$ is trustworthy, while sender $2$ is adversarial. The receiver first decodes sender $2$'s message, followed by sender $1$'s message. In this case, the decoding operator for sender $2$'s message interferes with the decoding of sender $1$'s message.

Theorems & Definitions (13)

• Definition 2.1
• Definition 2.2
• Definition 2.3
• Definition 2.4
• Theorem 3.1
• proof
• Theorem 3.2
• proof
• Theorem 3.3
• proof