Translating Bell Non-Locality to Prepare-and-Measure Scenarios under Dimensional Constraints

TL;DR

This paper develops a systematic method to translate bipartite Bell inequalities into prepare-and-measure tasks with dimensional constraints, enabling the adaptation of non-local certification protocols to sequential scenarios.

Contribution

It introduces a framework for translating Bell inequalities into dimensionally-bounded prepare-and-measure tasks, preserving key properties and broadening certification methods.

Findings

Identifies conditions for preserving quantum bounds during translation.

Proposes new experimentally-friendly certification protocols.

Establishes equivalences with existing prepare-and-measure protocols.

Abstract

Understanding the connections between different quantum information protocols has been proven fruitful for both theoretical insights and experimental applications. In this work, we explore the relationship between non-local and prepare-and-measure scenarios, proposing a systematic way to translate bipartite Bell inequalities into dimensionally-bounded prepare-and-measure tasks. We identify sufficient conditions under which the translation preserves the quantum bound and self-testing properties, enabling a wide range of certification protocols originally developed for the non-local setting to be adapted to the sequential framework of prepare-and-measure with a dimensional bound. While the dimensionality bound is not device-independent, it still is a practical and experimentally reasonable assumption in many cases of interest. In some instances, we find new experimentally-friendly certification protocols. In others, we demonstrate equivalences with already known prepare-and-measure protocols, where self-testing results were previously established using alternative mathematical methods. Our results unify different quantum correlation frameworks, and contribute to the ongoing research effort of studying the interplay between parallel and sequential protocols.