Quantum algorithmic information theory

Abstract

The agenda of quantum algorithmic information theory, ordered `top-down,' is the quantum halting amplitude, followed by the quantum algorithmic information content, which in turn requires the theory of quantum computation. The fundamental atoms processed by quantum computation are the quantum bits which are dealt with in quantum information theory. The theory of quantum computation will be based upon a model of universal quantum computer whose elementary unit is a two-port interferometer capable of arbitrary $U(2)$ transformations. Basic to all these considerations is quantum theory, in particular Hilbert space quantum mechanics.

latex, amsfonts; series of lectures given at the summer school "Chaitin Complexity and Applications", Mangalia, June 27th - July 6th, 1995, Mangalia, Romania

References in corpus (1)

• Quantum computation and complexity theory

Cited by in corpus (13)

• Quantum Kolmogorov Complexity
• Asymptotic Redundancies for Universal Quantum Coding
• Quantum Kolmogorov Complexity and the Quantum Turing Machine
• Algorithmic Information Theoretic Issues in Quantum Mechanics
• Prefix-free quantum Kolmogorov complexity
• Quantum Kolmogorov Complexity and Information-Disturbance Theorem
• The information-theoretical viewpoint on the physical complexity of classical and quantum objects and their dynamical evolution
• Law of Excluded Quantum Gambling Strategies
• The definition of a random sequence of qubits: from Noncommutative Algorithmic Probability Theory to Quantum Algorithmic Information Theory and back
• The No Cloning Theorem versus the Second Law of Thermodynamics
• Quantum substitutions of Pisot type, their quantum topological entropy and their use for optimal spacing
• Classification of the automorphisms of the noncommutative torus among the (chaotic and non-chaotic) shallow ones and the non-chaotic complex ones
• Second Quantized Kolmogorov Complexity