Quantum Channel Capacity Limits Defined for Adversarial Communication Networks

Researchers demonstrate that the communication capacity of fully arbitrarily varying channels—even with adversarial interference—equals that of simplified compound channels, utilising a novel minimax approach. This advancement bypasses conventional de Finetti reductions, accommodating jammers employing systems of any complexity and enabling improved channel characterisation.

The reliable transmission of quantum information necessitates robust methods to counter malicious interference. Researchers are now refining techniques to characterise the limits of communication channels when faced with adversaries employing complex ‘jamming’ signals. Cao, Yao, and Berta, from the Institute for Quantum Information at RWTH Aachen University, Germany, detail a new minimax approach in their paper, ‘Channel coding against quantum jammers via minimax’. This work circumvents limitations inherent in previous methods by avoiding reliance on de Finetti reductions – a mathematical technique used to simplify probabilistic models – and allows for the analysis of jammers utilising infinite-dimensional quantum systems. Their analysis demonstrates equivalence between the capacities of fully arbitrarily varying quantum channels (FQAVCs) and corresponding compound channels, even when confronted with general adversarial strategies.

Quantum Communication Limits Defined for Arbitrary Noise

Researchers have determined fundamental limits on reliable communication across quantum channels subject to completely unknown and fluctuating noise. These channels, termed fully arbitrarily varying quantum channels (FQAVCs), represent the most general and challenging scenario for quantum communication.

The study establishes a direct relationship between the communication capacity of an FQAVC and that of its corresponding compound channel. A compound channel is a simplified model where the noise distribution, while still unknown, is constrained to a specific set. This connection permits analysis of complex, unpredictable channels by leveraging the properties of their more tractable counterparts.

Critically, the research demonstrates that utilising pre-shared entanglement – a quantum correlation between communicating parties – or shared classical randomness does not increase the ultimate achievable communication rate across FQAVCs. This finding clarifies the limitations of these resources in the face of completely adversarial noise.

The team employed a minimax approach, rooted in game theory, to determine optimal coding strategies and establish tight upper and lower bounds on achievable communication rates. This methodology deliberately avoids reliance on de Finetti reductions – a technique used to simplify channel analysis by assuming a certain statistical structure – to accommodate the infinite-dimensional nature of the adversarial noise model.

The work provides a theoretical framework for understanding communication limits in the most general quantum noise scenarios, offering insights relevant to the development of robust quantum communication protocols.