Approximate and Exact Consistency of Histories

Abstract

The consistent histories formalism is discussed using path-projected states. These are used to analyse various criteria for approximate consistency. The connection between the Dowker-Halliwell criterion and sphere packing problems is shown and used to prove several new bounds on the violation of probability sum rules. The quantum Zeno effect is also analysed within the consistent histories formalism and used to demonstrate some of the difficulties involved in discussing approximate consistency. The complications associated with null histories and infinite sets are briefly discussed.

32 pages, revtex, no figures. Explanations improved, one proof extended. To appear Phys. Rev A 1st March 96

References in corpus (7)

• Classical Equations for Quantum Systems
• On the Consistent Histories Approach to Quantum Mechanics
• Quantum Logic and the Histories Approach to Quantum Theory
• Properties of Consistent Histories
• Environment--Induced Decoherence, Classicality and Consistency of Quantum Histories
• Decoherence produces coherent states: an explicit proof for harmonic chains
• Quantum-Mechanical Histories and the Uncertainty Principle. II. Fluctuations About Classical Predictability

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• On the Consistent Histories Approach to Quantum Mechanics
• Consistent Histories and Quantum Reasoning
• Quasiclassical Dynamics in a Closed Quantum System
• Somewhere in the Universe: Where is the Information Stored When Histories Decohere?
• Effects of Lévy noise on the dynamics of sine-Gordon solitons in long Josephson junctions
• The Objective Past of a Quantum Universe: Redundant Records of Consistent Histories
• Approximate Decoherence of Histories and 't Hooft's Deterministic Quantum Theory
• Quantum Prediction Algorithms
• Maximum Information and Quantum Prediction Algorithms