Contributions to the mathematical foundations of quantum information theory and stationary processes

Masahito Hayashi

Omar Fawzi

Giacomo Mauro D’Ariano, Andrei Yu. Khrennikov

This special issue is based on the contributions of a group of top experts in quantum foundations and quantum information and probability. It enlightens a number of interpretational, mathematical and experimental problems of quantum theory.

Guillaume Aubrun, Stanisław Szarek

Jincheng Zhang

This paper introduces a novel entropy concept – non-classical entanglement entropy – designed to quantify the complexity and information content of quantum entanglement states. Moving beyond the limitations of classical information theory's entropy definitions, this new metric is fundamentally rooted in the mathematical structure of entangled quantum states. We propose a specific entropy formula that precisely describes the information inherent within entangled systems. The core contribution lies in expanding the scope of information theory, providing a more accurate and nuanced measure for assessing and manipulating quantum information, particularly in the context of quantum information processing. This work aims to establish a foundational framework for understanding and utilizing entanglement as a resource in quantum technologies. ---

Nicolas Gisin, Florian Fröwis

Quantum non-locality has been an extremely fruitful subject of research, leading the scientific revolution towards quantum information science, in particular, to device-independent quantum information processing. We argue that the time is ripe to work on another basic problem in the foundations of quantum physics, the quantum measurement problem, which should produce good physics in theoretical, mathematical, experimental and applied physics. We briefly review how quantum non-locality contributed to physics (including some outstanding open problems) and suggest ways in which questions around macroscopic quantumness could equally contribute to all aspects of physics.This article is part of a discussion meeting issue 'Foundations of quantum mechanics and their impact on contemporary society'.