Simulating quantum systems using real Hilbert spaces

TL;DR

This paper introduces a method to simulate multipartite quantum systems using real Hilbert spaces, enabling local evolution and measurements, with applications to Bell inequalities and self-testing.

Contribution

It extends previous simulation techniques to include local evolution and measurements, applicable to both discrete and continuous quantum dynamics.

Findings

Successfully simulates local quantum evolution and measurements

Enables analysis of Bell inequalities with real Hilbert space models

Provides tools for self-testing quantum devices

Abstract

We develop a means of simulating the evolution and measurement of a multipartite quantum state under discrete or continuous evolution using another quantum system with states and operators lying in a real Hilbert space. This extends previous results which were unable to simulate local evolution and measurements with local operators and was limited to discrete evolution. We also detail applications to Bell inequalities and self-testing of quantum apparatus.