Capacity of Lossy Bosonic Channels Determined Under Semi-Classical Attacks

Understanding how to reliably transmit information through noisy channels remains a fundamental challenge in quantum communication, and recent work by Janis Nötzel and Florian Seitz, both from Technische Universität München, addresses this problem with a novel approach to analysing particularly challenging communication scenarios. The researchers investigate data transmission over ‘bosonic arbitrarily varying quantum channels’, which represent a worst-case model for signal degradation where an adversary actively attempts to disrupt communication. This study provides a crucial coding theorem and an explicit formula for calculating the maximum rate at which information can be sent reliably through such a channel, even when subject to deliberate interference, and importantly, demonstrates a connection between this capacity formula and a recently proposed inequality relating to entropy power. Establishing this limit is a significant step towards designing practical and secure quantum communication systems capable of withstanding sophisticated attacks.

Estimation Bounds and Probability Distributions

This document presents a rigorous mathematical analysis of estimation problems, focusing on establishing bounds and properties of probability distributions relevant to signal processing and information transmission. The core of the work involves a series of mathematical proofs, known as lemmas, that build upon each other to support a larger argument concerning optimal performance in communication or sensing systems. The research explores concepts from information theory, such as entropy and probability distributions, and connects to quantum information theory through the use of specific mathematical symbols. A key concept is sub-Gaussianity, a property of random variables that helps define the limits of estimation accuracy.

The document emphasizes the importance of permutation invariance, meaning the results remain consistent regardless of the order of certain elements. It establishes mathematical inequalities and bounds to define the performance limits of the system under consideration. This work provides a foundation for understanding the limits of estimation and coding in noisy environments, offering a framework for analyzing communication and sensing systems and informing the design of more efficient and reliable technologies.

Adversarial Jamming Limits with Common Randomness

Researchers have developed a new method for analyzing the capacity of quantum communication channels when faced with an adversary attempting to disrupt the transmission. Their approach involves transforming a complex attack into a more manageable form suitable for analysis, utilizing common randomness where both the sender and receiver employ shared random keys to mask their signals, effectively randomizing the attack. This randomization converts the attack into a combination of independent and identically distributed (i. i. d.

Dealing with the infinite-dimensional nature of quantum systems required careful consideration, and the researchers employed phase randomization to simplify the attack, transforming it into one composed of states that are mutually diagonal in a specific basis. By carefully controlling the local dimension of the jamming signal, the researchers connected the adversarial strategy to i. i. d.
Ultimately, the approach allows for a de-Finetti type of estimate, characterizing the structure of the jamming attack and relating it to the i. i. d. strategies required for applying compound codes. The team demonstrated that the effective jamming strategy has a specific structure, enabling them to establish fundamental limits on the capacity of the channel under adversarial conditions.

Quantum Channel Capacity with Adversarial Interference

Researchers have established a fundamental limit on the rate at which information can be reliably transmitted through noisy quantum channels, specifically those subject to interference from an adversary. This work focuses on a scenario where communication occurs over a beam splitter, with a legitimate sender and an interfering “jammer” both contributing signals, and a receiver observing only one of the outputs. The team has derived a formula for calculating the capacity of this channel, representing the maximum rate of reliable communication. The researchers demonstrate that determining the capacity involves finding the best possible probability distribution over encoding strategies, while simultaneously minimizing the impact of the jammer’s interference. Importantly, the team’s findings build upon and extend previous work in classical information theory, adapting concepts like entropy and entropy power inequalities to the quantum realm. The results demonstrate that, with the assistance of classical-quantum random encoding, the capacity can be determined by optimizing a specific entropic expression, paving the way for designing more robust and efficient communication systems.

Capacity Against Semi-Classical Jamming Attacks

This research establishes a fundamental capacity formula for transmitting information across lossy bosonic channels when subject to semi-classical jamming attacks. The work demonstrates how to calculate the maximum rate at which information can be reliably sent, even when an adversary attempts to disrupt the transmission by injecting carefully crafted signals. A key finding is the connection between this capacity formula and a recently proposed entropy power inequality, suggesting a deeper relationship between information theory and the properties of quantum systems. The authors successfully show that the jamming strategy employed by the adversary can be effectively reduced to a simpler form, allowing for the application of established coding techniques. This simplification relies on demonstrating that the adversary’s actions can be accurately described using permutation-invariant states, which are easier to analyze and counteract. The authors acknowledge that their analysis relies on certain approximations and bounds, which may introduce limitations on the precision of the calculated capacity.