Phys. Rev. Lett. 100, 210503 (2008) [4 pages]

Testing the Dimension of Hilbert Spaces

Abstract

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Nicolas Brunner¹, Stefano Pironio², Antonio Acin^2,3, 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

Received 6 February 2008; published 30 May 2008

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.

URL:

http://link.aps.org/doi/10.1103/PhysRevLett.100.210503

DOI:

10.1103/PhysRevLett.100.210503

PACS:

03.67.Mn, 03.65.Ta

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Phys. Rev. Lett. 100, 210503 (2008) [4 pages]

Testing the Dimension of Hilbert Spaces