The Nature of Information in Quantum Mechanics

Abstract

A suitable unified statistical formulation of quantum and classical mechanics in a *-algebraic setting leads us to conclude that information itself is noncommutative in quantum mechanics. Specifically we refer here to an observer's information regarding a physical system. This is seen as the main difference from classical mechanics, where an observer's information regarding a physical system obeys classical probability theory. Quantum mechanics is then viewed purely as a mathematical framework for the probabilistic description of noncommutative information, with the projection postulate being a noncommutative generalization of conditional probability. This view clarifies many problems surrounding the interpretation of quantum mechanics, particularly problems relating to the measuring process.

Additional comments, and some explanations rephrased. (Mostly in Sections 1 and 2.) Four references added. 19 pages

References in corpus (4)

• The quantum structure of spacetime at the Planck scale and quantum fields
• Quantum probabilities as Bayesian probabilities
• Quantum Foundations in the Light of Quantum Information
• Recurrence in Quantum Mechanics

Cited by in corpus (5)

• Quantum Mechanics as Quantum Information (and only a little more)
• Characterizing quantum theory in terms of information-theoretic constraints
• The Significance of Information in Quantum Theory
• Admissibility of truth assignments for quantum propositions in supervaluational logic
• Quantum Logic and Non-Commutative Geometry