The definition of a random sequence of qubits: from Noncommutative Algorithmic Probability Theory to Quantum Algorithmic Information Theory and back

2000/09/04 by Gavriel Segre, Segre, Gavriel
Computer Science · Mathematics · Physics and Astronomy · #Algorithm #Benford’s Law and Fraud Detection #Computability, Logic, AI Algorithms #Computational Complexity (cs.CC) #Computer science #Connection (principal bundle) #FOS: Computer and information sciences #FOS: Physical sciences #Information theory #Mathematical Physics (math-ph) #Mathematics #Noncommutative geometry #Physics #Probability theory #Pure mathematics #Quantum #Quantum Computing Algorithms and Architecture #Quantum Physics (quant-ph) #Quantum information #Quantum mechanics #Qubit #Random sequence #Sequence (biology) #Theoretical computer science #cs.CC #math-ph #math.MP #quant-ph

paper · pdf · doi:10.48550/arxiv.quant-ph/0009009

University of Pavia - Europe

openalex publication_date 2000/09/04 · arxiv created 2001/04/08 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

The issue of defining a random sequence of qubits is studied in the framework of Algorithmic Free Probability Theory.Its connection with Quantum Algorithmic Information Theory is shown

Citations

• An Invitation to von Neumann Algebras
• Quantum Probability for Probabilists
• Coding Theorems of Quantum Information Theory
• Quantum Complexity Theory
• The definition of random sequences
• Quantum theory, the Church–Turing principle and the universal quantum computer
• Simulating physics with computers
• Algorithmic Information Theory

Related

• Quantum Randomness and Nondeterminism
• The algorithmic randomness of quantum measurements
• A refinement of quantum mechanics by algorithmic randomness
• Noncommutative Martin-Lof randomness : on the concept of a random sequence of qubits
• Algorithmic Randomness and Kolmogorov Complexity for Qubits