Fundamental Concepts

Weisi Tang, Xin Luo

Matrix theory play a fundamental role in classical and quantum computing. Among this paper, we study the fundamental concepts of some matrices including unitary matrix and Hermitian matrix, which may convert some initial qubits into various kinds of qubits. We also explore the fundamental concept of eigenvalues. Furthermore, we input the concept of product vectors. Finally we use above-mentioned concepts examing the entanglement witness for verifying the entanglement in quantum computing and circuits.

Alexandre M. Zagoskin

Nicolas Brunner

This thesis is devoted to the study of quantum non-locality, in the framework of quantum information science. The research presented here includes both theoretical works on some fundamental concepts, such as the measurement process and quantum correlations, as well as some applications in modern quantum optics. As it is often the case in quantum information science, the joint study of fundamental notions and applications is very productive. While a better understanding of the fundamental concepts may lead to new applications, it happens also that applications shed new light on some fundamental notions...

Karl Blum

Diederik Aerts, Sandro Sozzo, Tomás Veloz

We recently performed cognitive experiments on conjunctions and negations of two concepts with the aim of investigating the combination problem of concepts. Our experiments confirmed the deviations (conceptual vagueness, underextension, overextension etc.) from the rules of classical (fuzzy) logic and probability theory observed by several scholars in concept theory, while our data were successfully modelled in a quantum-theoretic framework developed by ourselves. In this paper, we isolate a new, very stable and systematic pattern of violation of classicality that occurs in concept combinations. In addition, the strength and regularity of this non-classical effect leads us to believe that it occurs at a more fundamental level than the deviations observed up to now. It is our opinion that we have identified a deep non-classical mechanism determining not only how concepts are combined but, rather, how they are formed. We show that this effect can be faithfully modelled in a two-sector Fock space structure, and that it can be exactly explained by assuming that human thought is the superposition of two processes, a 'logical reasoning', guided by 'logic', and a 'conceptual reasoning', guided by 'emergence', and that the latter generally prevails over the former. All these findings provide new fundamental support to our quantum-theoretic approach to human cognition.

Karl Blum