Quantum Prediction Algorithms

TL;DR

This paper explores the challenge of selecting a single, natural consistent set in the consistent histories formulation of quantum mechanics, using Schmidt decomposition properties, and discusses the inherent difficulties in interpreting quantum theory precisely.

Contribution

It proposes algorithms based on Schmidt decomposition to select a unique consistent set, highlighting the conceptual and mathematical challenges involved.

Findings

Identifies issues in choosing a single consistent set in quantum histories

Proposes potential algorithms for set selection using Schmidt decomposition

Highlights difficulties in interpreting quantum theory through decoherence

Abstract

The consistent histories formulation of the quantum theory of a closed system with pure initial state defines an infinite number of incompatible consistent sets, each of which gives a possible description of the physics. We investigate the possibility of using the properties of the Schmidt decomposition to define an algorithm which selects a single, physically natural, consistent set. We explain the problems which arise, set out some possible algorithms, and explain their properties with the aid of simple models. Though the discussion is framed in the language of the consistent histories approach, it is intended to highlight the difficulty in making any interpretation of quantum theory based on decoherence into a mathematically precise theory.