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

authored by: Benjamin D.M. Jones, Roope Uola, Thomas Cope, Marie Ioannou, Sébastien Designolle, Pavel Sekatski, Nicolas Brunner
Abstract: 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 an alternative 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.
Organisation(s): Institute of Theoretical Physics
CRC 1227 Designed Quantum States of Matter (DQ-mat)
External Organisation(s): University of Geneva
University of Bristol
Type: Article
Journal: Physical Review A
Volume: 107
ISSN: 2469-9926
Publication date: 31.05.2023
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Atomic and Molecular Physics, and Optics
Electronic version(s): https://doi.org/10.48550/arXiv.2207.04080 (Access: Open)
https://doi.org/10.1103/PhysRevA.107.052425 (Access: Closed)

BibTeX

@article{141b41a95f624bd5b2b1405bba85a66c,
title = "Equivalence between simulability of high-dimensional measurements and high-dimensional steering",
abstract = "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 an alternative 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.",
author = "Jones, {Benjamin D.M.} and Roope Uola and Thomas Cope and Marie Ioannou and S{\'e}bastien Designolle and Pavel Sekatski and Nicolas Brunner",
note = "Funding Information: We acknowledge financial support from the Swiss National Science Foundation (Projects No. 192244, Ambizione No. PZ00P2-202179, and NCCR SwissMAP). B.D.M.J. acknowledges support from UK EPSRC (EP/SO23607/1). T.C. would like to acknowledge the funding Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany's Excellence Strategy EXC-2123 QuantumFrontiers Grant No. 390837967, as well as the support of the Quantum Valley Lower Saxony and the DFG through SFB Grant No. 1227 (DQ-mat).",
year = "2023",
month = may,
day = "31",
doi = "10.48550/arXiv.2207.04080",
language = "English",
volume = "107",
journal = "Physical Review A",
issn = "2469-9926",
publisher = "American Physical Society",
number = "5",
}