School on Advanced Topics in Quantum Information and Foundations

Organized by the Quantum Information Unit and the Yukawa Institute for Theoretical Physics, Kyoto University

To be held online from February 1 to 12, 2021

Description

The school on advanced topics in quantum information and foundations will include two courses. The first course will focus on a connection between matching theory and quantum information theory, recently unveiled by the lecturers, Prof. Péter E. Frenkel [Loránd Eötvös University (ELTE), Hungary] and Prof. Mihály Weiner [Budapest University of Technology and Economics (BME), Hungary], in proving a fundamental result in the field of classical information over quantum channels. The second course will explore cellular automata and operational probabilistic theories within the field of quantum foundations, and will be delivered by Prof. Paolo Perinotti (Pavia University, Italy).

Registration

Registrations are closed.

Invited lecturers

Program

First week (February 1 to 5, 2021)

Second week (February 8 to 12, 2021)

Syllabi

Information storage capacity, exact simulations, and the Supply--Demand Theorem

Péter E. Frenkel, Loránd Eötvös University (ELTE), Hungary, and Mihály Weiner, Budapest University of Technology and Economics (BME), Hungary

It is natural to compare physical systems for their ability to store information. However, the "storage capacity" of a system cannot be described by a single number. In general, deciding whether system A is better than system B depends on the specific task. Nevertheless, in some cases --- at least, from the point of view of writing in and reading out information from a single, uncoupled system --- one can show that system A can be used to make an exact simulation of system B, implying that in whatever sensible way one defines the storage capacity, it will never take a smaller value on A than on B.

In our minicourse we give an overview of some measures of information storage capacity of a system given in a general probabilistic framework. We show how the Supply--Demand Theorem known from matching theory can be used to give an upper bound on the number of classical bits required to exactly simulate a system (from this information storage capacity point of view). In particular we show that an n-level quantum system can always be simulated by an n-level classical system. Some further applications will also be discussed.

Based on arXiv:1304.5723 and arXiv:2101.10985.

Operational probabilistic theories and cellular automata: how I learned to stop worrying and love C* algebras

Paolo Perinotti, Pavia University

After introducing Operational Probabilistic Theories (OPT), we will review the basic concepts of the theory of Quantum Cellular automata, and extend the main definition to the wider context of OPTs. We will then discuss the notion of causal influence in OPTs, and use it to build the graph representing the causal relations between cells for a given cellular automaton. We will then define homogeneity in the absence of a background space, and show how homogeneity implies that the graph of causal connections is a Cayley graph of a group.

Organizer

The school is organized by Michele Dall'Arno, YITP, Kyoto University. Please feel free to contact me for any inquiry about the school.

The logo of Kyoto University by Source, Fair use. The logo of the Yukawa Institute for Theoretical Physics.

Latest update on February 13, 2021.