Abstract : In this talk, we introduce foundations of measurement theory in general quantum systems described by σ-finite von Neumann algebras. We define a condition called the normal extension property (NEP) and establish a one-to-one correspondence between CP instruments with the NEP and statistical equivalence classes of measuring processes. The concept of posterior states is also discussed to show that the NEP is equivalent to the existence of a strongly measurable family of posterior states for every normal state. Furthermore, we show the approximate realizability of CP instruments by measuring processes within arbitrarily given error limits. Lastly, we show uncertainty relations applicable to general quantum systems.

Gen Kimura
Title : Introduction to general information theory based on general probabilistic theories

Abstract :One of the recent trends in the fileds of quantum information science and the foundation of quantum theory is an investigation of operationally the most general information theory based on general probabilistic theories, generalizing classical and quantum information theories. It is expected to understand the inter relationships among physical principles and information processings. As one of its applications, for instance, we can discuss an unconditional secure key distribution without resort to quantum mechanics, thus having a stronger security than the quantum key distribution.
In this talk, we first introduce the general probabilistic theories (GPTs), which provide the most general framework of operationally valid probability. The emphasis is that we won't introduce mathematical structures a priori (as we usually do in the standard quantum theory) but we derive them as one of the natural representations based on operationally natural principles. Next, we discuss the general information theory based on GPTs. In particular, we show how entropy can be introduced in GPTs, and discuss its application to information gain and storage.

Norio Nawata
Title : Trace scaling automorphisms of certain stably projectionless C*-algebras

Abstract : Let W be a certain simple nuclear stably projectionless C*-algebra having trivial K-groups and a unique tracial state and no unbounded traces. We show that every trace scaling automorphism of W \otimes K has the Rohlin property. Moreover we shall discuss the classification problem for trace scaling automorphisms of W \otimes K.

Etsuo Segawa
Title : Construction and analysis of quantum walks

Abstract : Quantum walks have been intensively studied since quantum walks provide a positive effect to accomplish the quantum speed up in the quantum search algorithm in the beginning of 2000. Now a day, various kinds of quantum walk models are proposed from not only quantum information but also many research fields and becomes an interdisciplinary research field. In this talk, I will explain a fundamental construction of discrete-time quantum walks, which includes a lot of quantum walk models, and provide spectral analysis and its stochastic long time behavior of a special class of quantum walks.

Sergey Neshveyev
Title : Probabilistic boundaries of quantum random walks

Abstract : I will review the boundary theory of quantum random walks, which was initiated by Biane and Izumi in the 90s, and give some examples, generalizations and applications.

Koichi Shimada
Title : Maximal amenability of the generator subalgebra in q-Gaussian von Neumann algebras

Abstract : We give explicit examples of maximal amenable von Neumann subalgebras of the q-Gaussian von Neumann algebras. More precisely, the generator subalgebra is maximal amenable inside the q-Gaussian algebras for real numbers q　with |q|<1/9. We would like to show this based on Popa's theory. In order to achieve this, we construct a Riesz basis in the spirit of Radulescu.　This is a joint work with Sandeepan Parekh and Chenxu Wen.

Benoit Collins
Title : Highly entangled spaces through non random methods

Abstract :This talk is based on joint works with Mike Brannan, where we use techniques from free probability theory and quantum groups to produce subspaces of a tensor product of Hilbert space and quantum channels that are highly entangled.