SwissMAP Logo
Log in
  • About us
    • Organization
    • Professors
    • Senior Researchers
    • Postdocs
    • PhD Students
    • Alumni
  • News & Events
    • News
    • Events
    • Online Events
    • Videos
    • Newsletters
    • Press Coverage
    • Perspectives Journal
    • Interviews
  • Research
    • Basic Notions
    • Phase III Directions
    • Phases I & II Projects
    • Publications
    • SwissMAP Research Station
  • Awards, Visitors & Vacancies
    • Awards
    • Innovator Prize
    • Visitors
    • Vacancies
  • Outreach & Education
    • Masterclasses & Doctoral Schools
    • Mathscope
    • Maths Club
    • Athena Project
    • ETH Math Youth Academy
    • SPRING
    • Junior Euler Society
    • General Relativity for High School Students
    • Outreach Resources
    • Exhibitions
    • Previous Programs
    • Events in Outreach
    • News in Outreach
  • Equal Opportunities
    • Mentoring Program
    • Financial Support
    • SwissMAP Scholars
    • Events in Equal Opportunities
    • News in Equal Opportunities
  • Contact
    • Corporate Design
  • Basic Notions
  • Phase III Directions
  • Phases I & II Projects
  • Publications
  • SwissMAP Research Station

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

Benjamin D.M. Jones, Roope Uola, Thomas Cope, Marie Ioannou, Sébastien Designolle, Pavel Sekatski, Nicolas Brunner

8/7/22 Published in : 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.

Entire article

Phase I & II research project(s)

  • Quantum Systems

Fock-Goncharov dual cluster varieties and Gross-Siebert mirrors

Towards a minimal example of quantum nonlocality without inputs

  • Leading house

  • Co-leading house


The National Centres of Competence in Research (NCCRs) are a funding scheme of the Swiss National Science Foundation

© SwissMAP 2025 - All rights reserved