Spectrum Broadcast Structures from von Neumann type interaction Hamiltonians with continuous variables

TL;DR

This paper advances the mathematical understanding of Spectrum Broadcast Structures (SBS) in quantum systems, focusing on infinite-dimensional systems with continuous spectra and von Neumann interactions, revealing new theoretical insights.

Contribution

It extends SBS theory to infinite-dimensional systems with continuous spectra, addressing previously unexamined mathematical challenges in this context.

Findings

Mathematical framework for SBS with continuous spectra

Analysis of asymptotic convergence to SBS in infinite dimensions

Identification of new mathematical complications in the theory

Abstract

In this paper, we contribute to the mathematical foundations of the recently established theory of Spectrum Broadcast Structures (SBS). These are multipartite quantum states, encoding an operational notion of objectivity and exhibiting a more advanced form of decoherence. We study SBS and asymptotic convergence to SBS in the case of a central system interacting with N environments via the von Neumann-type measurement interactions, ubiquitous in the theory of open quantum systems. We will be focusing on the case where the system is modeled by an infinite-dimensional Hilbert space and the operators associated with the system in the Hamiltonian have purely continuous spectrum. Such a setup yields mathematical complications that have hitherto not been addressed in the theory of SBS.