An Information-Theoretic Approach to Quantum Theory, II: The Formal Rules of Quantum Theory

Abstract

In a companion paper (hereafter referred to as Paper I), we have presented an attempt to derive the finite-dimensional abstract quantum formalism from a set of physically comprehensible assumptions. In this paper, we formulate a correspondence principle, the Average-Value Correspondence Principle, that allows relations between measurement outcomes which are known to hold in a classical model of a system to be systematically taken over into the quantum model of the system. Using this principle, we derive the explicit form of the temporal evolution operator (thereby completing the derivation of the abstract quantum formalism begun in Paper I), and derive many of the formal rules (such as operator rules, commutation relations, and Dirac's Poisson bracket rule) that are needed to apply the abstract quantum formalism to model particular physical systems.

20 pages, 3 figures, revtex4. Comments welcome

References in corpus (6)

• Relational Quantum Mechanics
• Characterizing quantum theory in terms of information-theoretic constraints
• Operationally Invariant Information in Quantum Measurements
• Consistency, Amplitudes and Probabilities in Quantum Theory
• The Significance of Information in Quantum Theory
• Maximum predictive power and the superposition principle

Cited by in corpus (1)

• An Information-Theoretic Approach to Quantum Theory, I: The Abstract Quantum Formalism