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2008

Testing the Hilbert space dimension

Brunner, Nicolas, Pironio, Stefano, Acin, Antonio et al.

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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 describes 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.

Testing the Hilbert space dimension · Around

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One can always increase the dimension of the Hilbert space by adding useless extra dimensions. Thus, the relevant question here is to obtain the minimal dimension d d required for the given correlations

Cited in the paper.

T. Vertesi and K. Pal, arXiv:0712.4225, arXiv:0712.4320

Cited in the paper.

S. Pironio, in preparation

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