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The Fields Institute for Research in Mathematical Sciences

The Copmutational Complexity Conference (CCC) aims to foster research in all areas of computational complexity theory, studying the absolute and relative power of computational models under resource constraints. Typical models include deterministic, nondeterministic, randomized, and quantum models; uniform and nonuniform models; Boolean, algebraic, and continuous models. Typical resource constraints involve time, space, randomness, program size, input queries, communication, and entanglement; worst-case as well as average case. Other, more specific, topics include: probabilistic and interactive proof systems, inapproximability, proof complexity, descriptive complexity, and complexity-theoretic aspects of cryptography and machine learning. The conference also encourages results from other areas of computer science and mathematics motivated by computational complexity theory.

Banff International Research Station for Mathematical Innovation and Discovery (BIRS)

Information theory aims to find mathematically precise answers to fundamental questions such as how information is stored, processed, or sent reliably through noisy communication links. Towards the end of the 20th century, researchers started asking how these information-processing tasks change when information is encoded in systems exhibiting quantum-mechanical behavior. Remarkably, features of quantum mechanics such as the superposition principle and entanglement give rise to phenomena in information theory that cannot be realized with classical information-processing systems. Their discovery has led to the creation of the now thriving field of quantum information theory. A cornerstone of quantum information theory is the principle of non-additivity of information measures. Roughly speaking, non-additivity occurs if a communication resource becomes more powerful when used repeatedly or in conjunction with another resource. On the one hand, non-additivity effects are desirable as they push the limits of faithfully communicating information. On the other hand, they complicate an exact characterization of these limits in both mathematical and computational terms. Our workshop gathers experts from all areas of quantum information theory, with the goal of shedding further light on, and identifying new methods to study, the nature of non-additivity phenomena in quantum information-processing systems.