Beyond IID in Information Theory 8

"Beyond IID in Information Theory" started as a workshop in Cambridge, UK seven years ago, organized 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 and quantum information, all the way to quantum thermodynamics and other resource theories.

Quantum Shannon theory is arguably the core of the new “physics of information,” which has revolutionized our understanding of information processing by demonstrating new possibilities that cannot occur in a classical theory of information. It is also a very elegant generalization 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 10-25 years have seen a plethora of new results and methods. Two of the most striking 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.

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-, Rényi-, 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.

The whole area is extremely dynamic, as the success of previous "Beyond IID" workshops has shown.

Description:

The present workshop, the eighth in a series that started in 2013 in Cambridge, will bring together specialists and students of classical and quantum Shannon theory, of cryptography, mathematical physics, thermodynamics, etc., in the hope to foster collaboration in this exciting field of one-shot information theory and its applications. The plan is to have a modest number of talks over the course of the week. Participation is open to all.

Topics:

The topics covered under "Beyond IID" include but are not limited to the following:

• Finite block length coding

• Second, third, and fourth order analysis

• Strong converses

• Quantum ​Shannon theory

• Cryptography and quantum cryptography

• New information tasks

• One-shot information theory and unstructured channels

• Information spectrum method

• Entropy inequalities

• Non-standard entropies (e.g. Rényi entropies, min-entropy, ...)

• Matrix analysis

• Thermodynamics

• Resource theories of asymmetry

• Generalized resource theories

• Physics of information