Information Theory Clarifies Limits to How Efficiently Computers Can Process Data

Researchers are increasingly focused on understanding the fundamental limits of computation and information processing. Nikolai Miklin from the Institute for Quantum-Inspired and Quantum Optimization at Hamburg University of Technology, working with Prabhav Jain and Mariami Gachechiladze from the Department of Computer Science at Technical University of Darmstadt, present new communication complexity bounds derived from the principle of information causality. This collaborative work, also involving colleagues at the Institute for Applied Physics, Technical University of Darmstadt, introduces an information-theoretic approach to one-way complexity, simplifying existing lower bounds for several functions and yielding novel results. Significantly, the team demonstrate that their extended information causality principle is at least as robust as the principle of non-trivial complexity when assessing correlations in Bell experiments, establishing a fresh perspective on the interplay between information theory and the foundations of quantum mechanics.

This work introduces an extended statement of the information causality principle, a concept rooted in the axioms of mutual information, to derive lower bounds on the communication required for collaborative problem-solving between parties with distributed information. Communication complexity, which measures the minimal communication needed for two or more parties to jointly compute a function with distributed inputs, serves as a critical lens for examining the capabilities and limitations of quantum mechanics in information processing. The team’s approach leverages shared entanglement, a uniquely quantum resource, to explore the boundaries between classical and quantum communication efficiency. This allows for a unified analysis applicable to both entanglement-assisted classical communication and direct quantum communication, with the findings suggesting that quantum advantages in communication complexity are subject to inherent limitations. The investigation builds upon the established information causality principle, previously applied to bounding quantum correlations in Bell experiments, and extends its reach to the realm of distributed computing. A rigorous information-theoretic framework underpinned this work, beginning with the application of mutual information axioms to analyse one-way complexity. This approach allowed the researchers to derive an extended statement of the information causality principle, central to understanding limits in information processing. By focusing solely on mutual information, the study sidestepped complexities inherent in other methods, offering a streamlined path to recovering established lower bounds on complexity for various functions. The investigation then extended this principle to the realm of distributed computation, specifically examining scenarios involving one-way entanglement-assisted classical communication. A key methodological choice was the adoption of the teleportation protocol, which facilitated the translation of bounds derived from entanglement-assisted communication to one-way quantum communication, with a maximum factor of two difference. This protocol was selected for its efficiency in transmitting quantum states, enabling a direct comparison between classical and quantum communication complexities. The researchers meticulously constructed a model where Alice and Bob receive random inputs, with Alice transmitting a limited number of bits to Bob, who then attempts to determine the function’s value. To assess the strength of the extended information causality principle, the study established a connection to Bell nonlocality and the principle of non-trivial communication complexity. The researchers leveraged the concept of Popescu-Rohrlich (PR) boxes, representing maximally correlated states, to demonstrate that the principle implies the existence of functions requiring communication complexity that scales with input size. This connection was established through a detailed analysis of how correlations attainable in Bell experiments are bounded by the proposed principle, providing a robust validation of its theoretical strength. The work deliberately considered total functions, where inputs x and y can take any value, rather than restricting the analysis to promised inputs. The extended information causality principle recovers known lower bounds on communication complexities for a range of functions with a simplified approach and yields novel results. Specifically, this research demonstrates that the principle successfully bounds the communication required to compute functions in a bipartite scenario utilising one-way entanglement-assisted classical communication. The study establishes a direct link between this principle and the principle of non-trivial communication complexity, proving the former is at least as strong as the latter in bounding quantum correlations observable in Bell experiments. Analysis reveals that for certain functions, the research recovers previously established asymptotically tight lower bounds on communication complexity using considerably more streamlined arguments. This simplification is achieved by focusing solely on the axioms of mutual information, offering a more elegant and direct pathway to derive these bounds. Furthermore, the work generates new results for functions where existing bounds were less precise or absent, expanding the understanding of fundamental limits in distributed computing. The implications extend to scenarios involving distributed correlations, such as those exhibited by Popescu-Rohrlich (PR) boxes, where any function can theoretically be computed with a single bit of communication regardless of input size. By establishing the principle of non-trivial communication complexity, the research asserts that functions must exist whose communication complexity scales with input size, thereby constraining the potential for such extreme efficiency. This connection between information-theoretic principles and the limitations of quantum correlations provides a new framework for exploring the boundaries of quantum technologies. This study establishes a novel pathway for exploring the fundamental limits of quantum technologies from an information-theoretic perspective, offering insights that are relevant not only to foundational quantum physics but also to the development of practical quantum communication and computation systems. The findings have implications for areas such as minimal models of computation and data structures, potentially guiding the design of more efficient and robust quantum algorithms and protocols. By providing a more refined understanding of the trade-offs between communication, entanglement, and computational power, this research contributes to the ongoing effort to harness the full potential of quantum information processing. Scientists have long sought to understand the fundamental limits of computation, and this work offers a compelling new angle on that enduring quest. Establishing robust boundaries on what is computationally possible requires a framework that doesn’t rely on specific hardware, but instead on the inherent properties of information itself. This research achieves precisely that by grounding complexity, a measure of computational difficulty, in the axioms of mutual information. The resulting extended information causality principle provides a surprisingly elegant way to derive known limits and, crucially, to push beyond them. Its connection to Bell experiments, demonstrating its strength in bounding correlations, is particularly noteworthy, suggesting a deeper link between quantum nonlocality and the very fabric of computational possibility. However, the framework remains theoretical; translating these information-theoretic bounds into practical improvements in computational devices is a significant challenge. Moreover, the precise role of noise and decoherence has yet to be fully explored within this new context. Future work might focus on applying these principles to specific computational problems, or on investigating how they might inform the design of more robust and efficient communication protocols. Ultimately, this is a step towards a more unified understanding of information, computation, and the physical world.