Graph-theoretic approach to dimension witnessing

TL;DR

This paper introduces a graph-theoretic method for quantum dimension witnessing, enabling the certification of high quantum dimensions with minimal measurement events, advancing quantum information theory.

Contribution

It presents a novel graph-based framework for quantum dimension witnessing in scenarios with one preparation and multiple measurements, including the identification of new high-dimension witnesses.

Findings

Developed graph-theoretic tools for quantum dimension certification

Identified new quantum dimension witnesses capable of certifying arbitrarily high dimensions

Demonstrated the effectiveness of the approach with minimal measurement events

Abstract

A fundamental problem in quantum computation and quantum information is finding the minimum quantum dimension needed for a task. For tasks involving state preparation and measurements, this problem can be addressed using only the input-output correlations. This has been applied to Bell, prepare-and-measure, and Kochen-Specker contextuality scenarios. Here, we introduce a novel approach to quantum dimension witnessing for scenarios with one preparation and several measurements, which uses the graphs of mutual exclusivity between sets of measurement events. We present the concepts and tools needed for graph-theoretic quantum dimension witnessing and illustrate their use by identifying novel quantum dimension witnesses, including a family that can certify arbitrarily high quantum dimensions with few events.