Universal Preparability of States and Asymptotic Completeness

TL;DR

This paper introduces the concept of universal preparability of states in quantum systems, providing criteria for when all states can be prepared from any initial state, and links this to asymptotic completeness in non-commutative Markov processes.

Contribution

It defines universal preparability for states on von Neumann algebras and establishes its equivalence with asymptotic completeness under certain conditions.

Findings

Criteria for universal preparability in non-commutative birth and death processes.

Development of the theory of tight sequences and stationary states.

Universal preparability is equivalent to asymptotic completeness with stationary faithful states.

Abstract

We introduce a notion of universal preparability for a state of a system, more precisely: for a normal state on a von Neumann algebra. It describes a situation where from an arbitrary initial state it is possible to prepare a target state with arbitrary precision by a repeated interaction with a sequence of copies of another system. For $\mathcal{B}(\mathcal{H})$ we give criteria sufficient to ensure that all normal states are universally preparable which can be verified for a class of non-commutative birth and death processes realized, in particular, by the interaction of a micromaser with a stream of atoms. As a tool the theory of tight sequences of states and of stationary states is further developed and we show that in the presence of stationary faithful normal states universal preparability of all normal states is equivalent to asymptotic completeness, a notion studied earlier in connection with the scattering theory of non-commutative Markov processes.