Symmetry and Natural Quantum Structures for Three-Particles in One-Dimension

TL;DR

This paper explores how symmetries in three-particle one-dimensional quantum models lead to natural structures that facilitate quantum information processing and deepen understanding of quantum few-body physics.

Contribution

It introduces a framework linking symmetries to quantum structures like tensor products, enhancing the interpretation and manipulation of three-particle quantum systems.

Findings

Symmetries induce meaningful collective observables.

Observable structures guide quantum information processing.

Framework applies across integrable and chaotic regimes.

Abstract

How do symmetries induce natural and useful quantum structures? This question is investigated in the context of models of three interacting particles in one-dimension. Such models display a wide spectrum of possibilities for dynamical systems, from integrability to hard chaos. This article demonstrates that the related but distinct notions of integrability, separability, and solvability identify meaningful collective observables for Hamiltonians with sufficient symmetry. In turn, these observables induce tensor product structures on the Hilbert space that are especially useful for storing and processing quantum information and provide guidance to interpretation and phenomenology of quantum few-body physics.