Testing the Dimension of Hilbert Spaces

Nicolas Brunner, Stefano Pironio, Antonio Acin, Nicolas Gisin, André Allan Méthot, and Valerio Scarani
Phys. Rev. Lett. 100, 210503 – Published 30 May 2008

Abstract

Given a set of correlations originating from measurements on a quantum state of unknown Hilbert space dimension, what is the minimal dimension d necessary to describe such correlations? We introduce the concept of dimension witness to put lower bounds on d. This work represents a first step in a broader research program aiming to characterize Hilbert space dimension in various contexts related to fundamental questions and quantum information applications.

  • Figure
  • Received 6 February 2008

DOI:https://doi.org/10.1103/PhysRevLett.100.210503

©2008 American Physical Society

Authors & Affiliations

Nicolas Brunner1, Stefano Pironio2, Antonio Acin2,3, Nicolas Gisin1, André Allan Méthot1, and Valerio Scarani4

  • 1Group of Applied Physics, University of Geneva, Geneva, Switzerland
  • 2ICFO-Institut de Ciencies Fotoniques, Castelldefels (Barcelona), Spain
  • 3ICREA-Institució Catalana de Recerca i Estudis Avançats, Barcelona, Spain
  • 4Centre for Quantum Technologies and Department of Physics, National University of Singapore, Singapore

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Issue

Vol. 100, Iss. 21 — 30 May 2008

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