Equivalence between simulability of high-dimensional measurements and high-dimensional steering

• Published in: arXiv.org
• Main Authors: Jones, Benjamin D M, Uola, Roope, Cope, Thomas, Ioannou, Marie, Designolle, Sébastien, Sekatski, Pavel, Brunner, Nicolas
• Format: Paper Journal Article
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 08.07.2022
• Subjects: Dimensional measurement; Entangled states; Incompatibility; Physics - Quantum Physics; Schmidt number; Steering
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.2207.04080

The effect of quantum steering arises from the judicious combination of an entangled state with a set of incompatible measurements. Recently, it was shown that this form of quantum correlations can be quantified in terms of a dimension, leading to the notion of genuine high-dimensional steering. While this naturally connects to the dimensionality of entanglement (Schmidt number), we show that this effect also directly connects to a notion of dimension for measurement incompatibility. More generally, we present a general connection between the concepts of steering and measurement incompatibility, when quantified in terms of dimension. From this connection, we propose a novel twist on the problem of simulating quantum correlations. Specifically, we show how the correlations of certain high-dimensional entangled states can be exactly recovered using only shared randomness and lower-dimensional entanglement. Finally, we derive criteria for testing the dimension of measurement incompatibility, and discuss the extension of these ideas to quantum channels.