Testing the Hilbert space dimension
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 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.
- Publication:
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arXiv e-prints
- Pub Date:
- February 2008
- DOI:
- 10.48550/arXiv.0802.0760
- arXiv:
- arXiv:0802.0760
- Bibcode:
- 2008arXiv0802.0760B
- Keywords:
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- Quantum Physics
- E-Print:
- 4 pages, 1 figure