Testing the dimension of Hilbert spaces |
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| Authors: | Brunner Nicolas Pironio Stefano Acin Antonio Gisin Nicolas Méthot André Allan Scarani Valerio |
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| Institution: | Group of Applied Physics, University of Geneva, Geneva, Switzerland. |
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| 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. |
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