The preparation of states in quantum mechanics (Q2804963)

In this paper, there is discussion about possible ways of preparation of a quantum mechanical system, \(S\), in a specific initial state of interest according to given limitations and conditions. There are several methods that solve this problem and the paper presents a discussion based on three distinct methods of state preparation (but mostly focuses on one related to weak interaction with a dispersive environment). Proposed ideas are explained basing on the concrete example of a system \(S\) with a finite-dimensional Hilbert space of pure state vectors considered here as a simple caricature of a very heavy ``atom'' coupled to a free massless scalar quantum field. In successive sections of this paper we have considerations that are related to: (i) quantum state preparation via weak interaction with a dispersive environment, (ii) preparation of states via adiabatic evolution, (iii) state preparation via duplication of systems and state selection. Each of these methods is described in Part A Sections 1--3 and then used for explanation of model description. Investigations are based on a proposed theorem with necessary proofs for both: single particle and many ``photons''.