Abstracts of Talks
A. Baltag and S. Smets, When Dynamic Quantum Logic and Dynamic Epistemic Logic meet
Abstract: We present a unified logical framework in which we bring together the work on Dynamic Quantum Logic and the work on Dynamic Epistemic Logic.
We use this setting to analyze and reason about both classical and quantum information flow. In particular we will pay attention to specific agent-based quantum protocols and scenarios involving on the one hand the non-classical behavior of quantum systems and on the other hand the epistemic states, the communication and observations made by classical agents. We will pay attention to the classical epistemic effects that we observe when agents use both classical and quantum communication.
M. Bosyk and M. Losada, Quantum Resource Theories and the Majorization Relation
Abstract: Majorization provides a way to partial order a set of finite dimensional probability vectors and, as such, arises naturally when one deals with finite dimensional quantum states. Here, we present implications of the theory of majorization into some quantum resources theories.
M. Dalla Chiara, Quantum Computational Logics, Logical Self-references and Quantum
Abstract: Quantum computational logics are new forms of quantum logic that have been inspired by quantum computation theories. We investigate the possibility of logical self-references for some versions of quantum computational logic, formalized in a weak first-order language. We show how these logics can express their own truth-concept, avoiding the liar-paradox.
D. Fazio and A. Ledda, The Generalized Orthomodularity Property: Configurations and Pastings
Abstract: We introduce the generalized orthomodularity property for orthoposets. A forbidden configurations characterization will be provided. As a consequence, we obtain Greechie’s theorems as straightforward corollaries as well as an order-theoretical explanation of the coherence law for several classes of effect
algebras.
Federico Holik, Global States of Collections of Arbitrary Random Variables
Abstract:Contextuality is one of the characteristic traits of quantum theory. Understanding this quantum feature is central for the development of quantum information theory. The description of a quantum system involves a collection of incompatible measurement contexts. Each context can be seen as a classical random variable, defined by a complete set of commuting observables. But it turns out that contexts are intertwined: quantum probabilistic models can be described as very specific pastings of Boolean algebras, which are globally non-Boolean. States are represented by density operators that define global states, and give place to classical probabilities when restricted to the maximal Boolean subalgebras associated to measurement contexts. The characterization of the peculiar pasting occurring in the quantum domain has been a topic of much research, and is related to the understanding of quantum contextuality. In this talk we discuss different techniques for combining collections of (possibly non-compatible) random variables in such a way that one obtains -as in the quantum case- a global state that yields classical probabilities when restricted to the local Boolean subalgebras. After commenting different approaches related to the possibility of using negative probabilities, we address the well known problem of pasting families of Boolean algebras. We discuss some of our findings with regard to the problem of defining global objects representing states of contextual probabilistic theories.
R. Giuntini and F. Paoli, Paraorthomodular Brouwer-Zadeh* lattices (PBZL*)
Abstract: The variety of PBZ*-lattices is an abstract algebraic counterpart of the strucure of all effects of a given complex separable Hilbert space, endowed with the spectral ordering instead of the usual ordering defined via the Born rule. This class of algebras is motivated, from a physical viewpoint, by the fact that
it reproduces at an abstract level the collapse of several notions of sharp physical property that is observed in the concrete physical model of effects; from an algebraic viewpoint, moreover, it can be viewed as an unsharp generalisation of orthomodular lattices that also covers certain expansions of Kleene lattices and, consequently, may have some potential interest for many-valued logics of partial information. We will survey the basic structure theory of PBZ*-lattices (central elements, ideal theory, embedding results), the structure of its lattice of subvarieties, some constructions (horizontal sums, ordinal sums), and the relationships between PBZ*-lattices and other classes of algebras motivated by quantum logic, modal logic and many-valued logic.
G. Sergioli and R. Giuntini, A Quantum Inspired Approach to Binary ClassificationI
Abstract: In this talk we describe a novel approach to the standard binary classification process, inspired by quantum information theory. We discuss the advantages of this new model and show some real application.
Reference: "G. Sergioli, R. Giuntini, H. Freytes (2019). A new Quantum Approach to binary Classification. PLoS ONE, ISSN:1932-6203, 14(5): e0216224."
S. Zhong, Quantum States - An Analysis via the Orthogonality Relation
Abstract: In this talk, I will discuss an approach in the mathematical foundations of quantum theory which is based on the orthogonality relation between (pure) states of a quantum system. First, I will argue via a representation theorem that the essentials of this relation in quantum theory are captured in five conditions on a binary relation. Second, I will discuss how the states and the orthogonality relation of a bipartite quantum system can be represented by the states and the orthogonality relations of its two subsystems. This leads to an abstract counterpart of the tensor product construction between two Hilbert spaces which relies on a characterization of linear maps of trace zero.