\u00abBeyond IID in Information Theory\u00bb started as a workshop in Cambridge three years ago, organised by Nilanjana Datta and Renato Renner as a forum for the growing interest in information theoretic problems and techniques beyond the strict asymptotic limit, and aimed at bringing together researchers from a range of different backgrounds, ranging from coding theory, Shannon theory in the finite block length regime, one-shot information theory, cryptography, quantum information, all the way to quantum thermodynamics and other resource theories.
Quantum Shannon theory is arguably the core of the new \u201cphysics of information,\u201d which has revolutionised our understanding of information processing by demonstrating new possibilities that cannot occur in a classical theory of information. It is also a very elegant generalisation, indeed extension, of Shannon’s theory of classical communication. The origins of quantum Shannon theory lie in the 1960s, with a slow development until the 1990s when the subject exploded; the last 10-15 years have seen a plethora of new results and methods. Two of the most striking recent discoveries are that entanglement between inputs to successive channel uses can enhance the capacity of a quantum channel for transmitting classical data, and that it is possible for two quantum communication channels to have a non-zero capacity for transmitting quantum data, even if each channel on its own has no such quantum capacity.<\/p>\n
In recent years, both in classical and quantum Shannon theory, attention has shifted from the strictly asymptotic point of view towards questions of finite block length. For this reason, and fundamentally, there is a strong drive to establish the basic protocols and performance limits in the one-shot setting. This one-shot information theory requires the development of new tools, in particular non-standard entropies and relative entropies (min-, R\u00e9nyi-, hypothesis testing), both in the classical and quantum setting. These tools have found numerous applications, ranging from cryptography to strong converses, to second and third order asymptotics of various source and channel coding problems. A particularly exciting set of applications links back to physics, with the development of a resource theory of thermodynamic work extraction and more generally of state transformations. Physicists have furthermore found other resource theories, for instance that of coherence and that of asymmetry, which are both relevant to the thermodynamics of quantum systems and interesting in their own right.<\/p>\n
The whole area is extremely dynamic, as the success of three previous \u00abBeyond IID\u00bb workshops has shown.<\/p>\n