A Theory of Quantum Preparation

TL;DR

This paper develops a comprehensive theoretical framework for quantum preparation, analyzing key entities involved in the process and distinguishing between dynamical and geometrical preparators, with implications for understanding quantum measurement mechanisms.

Contribution

It introduces a general theory of quantum preparators based on four fundamental entities, expanding the conceptual understanding of quantum state preparation processes.

Findings

Identifies four key entities in quantum preparation: composite-system state, triggering event, conditional state, and unitary evolution.

Distinguishes between dynamical and geometrical preparators within the same theoretical framework.

Discusses the concepts of conditional states and retrospective apparent ideal occurrence in detail.

Abstract

Based on an analysis of two conventional preparators, the Stern-Gerlach and the hole-in-the-screen ones, it is argued that four entities can be taken as the basic ingredients of a rather general theory of a quantum preparator. These are the composite-system (object plus preparator) state coming about as a result of a suitable interaction between the subsystems, a suitable preparator projector called the triggering event, the conditional quantum state (density operator) of the quantum object coming about as a consequence of the occurrence of the triggering event on the preparator, and, finally, a unitary evolution operator of the object subsystem acting after preparation. The concepts of a general conditional state and of retrospective apparent ideal occurrence (which appears in the theory) are discussed in considerable detail. Ideal occurrence and the selective L\"{u}ders formula, which are made use of, are reviewed. Dynamical and geometrical preparators are distinguished in the general theory. They are described by the same entities in the same way, but in terms of different physical mechanisms from the point of view of standard interpretation with collapse.