Quantum information science is one of the most dynamic, technologically promising, and intellectually exciting areas of today’s research landscape. Indeed, despite a modern history of 20 years (and the earliest work going back well into the 1960s), it still displays enormous potential for growth, with many interesting research avenues wide open. The field has benefited from having input from physicists, mathematicians, computer scientists, and electrical engineers, all of whom have relevant expertise to shape this subject.
This workshop will concentrate on quantum as well as classical Shannon theory, and the main goal is to broaden the application of this field to quantum and classical communication regimes in which the traditional assumptions no longer apply. For example, we would like to increase our understanding of communications in a more practically relevant regime involving only hundreds or thousands of bits or qubits. Furthermore, the traditional formulation of quantum or classical Shannon theory establishes fundamental bounds on rates that are achievable with a given resource in the asymptotic independent and identically distributed (i.i.d.) regime, in which an arbitrarily large number of uncorrelated instances of a given resource are allowed to be available. The aim of this workshop is to focus on understanding the following question in more detail:
"If one specifies an error tolerance no larger than some error ϵ > 0 and allows for using n instances of a given resource, what communication rates are achievable?"
Clearly, having good general answers to various instances of this question would represent not merely an incremental advance, but rather would be conceptually rich and directly relevant for practical implementations of quantum communication devices. Questions of the above form are also technically challenging, so that they should spark interest from both the theoretical quantum information and mathematical communities, and we expect new mathematical tools and techniques to emerge to address them. The time is ripe for a workshop to be held on this topic. Some major developments that have led the field of quantum Shannon theory to this point are the following:
- "One-shot" quantum information tasks, whose characterization in terms of (smooth) min- and max-entropies gives rise to a whole calculus of new quantities
- The quantum information spectrum method
- The finite blocklength approach developed in classical information theory and very recent advances in this area for quantum information theory
- Tools for analyzing channels with memory
- Strong converse theorems
- Classification and axiomatization of relative entropy measures
We are still far away from a complete picture, but at the same time significant recent progress suggests that major breakthroughs are within reach. This makes the whole area one of the hottest in quantum and classical information theory. One of the main goals of this workshop is to bring together researchers interested in these topics (both quantum and classical information theorists) to participate in focused discussions about them.
Previous editions of the workshop:
- Beyond i.i.d. in information theory I, Cambridge, UK (8-11 January 2013)
- Beyond i.i.d. in information theory II, University Town, CQT-NUS, Singapore (21-23 May 2014)
- Beyond i.i.d. in information theory III, BIRS, Alberta, Canada (5-11 July 2015)
