Quantum Probability and Randomness

• Main Author: Khrennikov, Andrei (auth)
• Other Authors: Svozil, Karl (auth)
• Format: Electronic Book Chapter
• Language: English
• Published: MDPI - Multidisciplinary Digital Publishing Institute 2019
• Subjects: irreducible randomness; quantum-like models for social stochasticity; partially defined algebras; indeterminism; protocol; Gram-Schmidt process; three-qubit random states; complementarity; entanglement classes; maximization of quantum conditional min-entropy; random numbers; quantum computation; MMP hypergraphs; quantum information theory; quasigroups; potentiality; random number generators; social energy; social thermodynamics; quantum dynamics; probability; entanglement; quantum foundations; quantum technology; vacuum state; quantum contextuality; orthogonality; quantum information; correlations; entanglement polytope; causation; quantum-like models; operational approach; reality; Borel normality; Bell inequalities; Copenhagen interpretation; social laser; quantum entanglement; algebra; Bose-Einstein statistics; realism; epistemic operations; quantum random number; information interpretation of quantum theory; viable cultures; master equation for socio-information excitations; entropy; quantum logics; qubits; holistic semantics; Bayesian inference; uncertainty relations; Bayes' formula; Kochen-Specker sets; model selection; quantum logic; groups; randomness; Greechie diagrams; causality; indefiniteness; probability representation; algorithmic complexity; resonator of social laser; bandwagon effect; contextuality; quantum probability; geometry; social atom; bit commitment; anisotropic invariants; quantum information field
• Online Access: DOAB: download the publication; DOAB: description of the publication

The last few years have been characterized by a tremendous development of quantum information and probability and their applications, including quantum computing, quantum cryptography, and quantum random generators. In spite of the successful development of quantum technology, its foundational basis is still not concrete and contains a few sandy and shaky slices. Quantum random generators are one of the most promising outputs of the recent quantum information revolution. Therefore, it is very important to reconsider the foundational basis of this project, starting with the notion of irreducible quantum randomness. Quantum probabilities present a powerful tool to model uncertainty. Interpretations of quantum probability and foundational meaning of its basic tools, starting with the Born rule, are among the topics which will be covered by this issue. Recently, quantum probability has started to play an important role in a few areas of research outside quantum physics—in particular, quantum probabilistic treatment of problems of theory of decision making under uncertainty. Such studies are also among the topics of this issue.