The collapse of a quantum state as a joint probability construction

Abstract

The collapse of a quantum state can be understood as a mathematical way to construct a joint probability density even for operators that do not commute. We can formalize that construction as a non-commutative, non-associative collapse product that is nonlinear in its left operand as a model for joint measurements at timelike separation, in part inspired by the sequential product for positive semi-definite operators. The familiar collapse picture, in which a quantum state collapses after each measurement as a way to construct a joint probability density for consecutive measurements, is equivalent to a no-collapse picture in which Lüders transformers applied to subsequent measurements construct a Quantum-Mechanics--Free-Subsystem of Quantum Non-Demolition operators, not as a dynamical process but as an alternative mathematical model for the same consecutive measurements. The no-collapse picture is particularly simpler when we apply signal analysis to millions or billions of consecutive measurements.

v4 has the same section numbers, equation numbers, and figure numbers as in the Published Version, but pagination is different

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Cited by in corpus (3)

• The Quantum Measurement Problem: A Review of Recent Trends
• Quantum Mechanics: Statistical Balance Prompts Caution in Assessing Conceptual Implications
• Connecting Commutativity and Classicality for Multi-Time Quantum Processes