Witnessing Irreducible Dimension.
- Cong W Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543, Singapore.
- Cai Y Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543, Singapore.
- Bancal JD Quantum Optics Theory Group, Department of Physics, University of Basel, Klingelbergstrasse 82, 4056 Basel, Switzerland.
- Scarani V Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543, Singapore.
- 2017-09-28
Published in:
- Physical review letters. - 2017
English
The Hilbert space dimension of a quantum system is the most basic quantifier of its information content. Lower bounds on the dimension can be certified in a device-independent way, based only on observed statistics. We highlight that some such "dimension witnesses" capture only the presence of systems of some dimension, which in a sense is trivial, not the capacity of performing information processing on them, which is the point of experimental efforts to control high-dimensional systems. In order to capture this aspect, we introduce the notion of irreducible dimension of a quantum behavior. This dimension can be certified, and we provide a witness for irreducible dimension four.
- Language
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- English
- Open access status
- green
- Identifiers
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- DOI 10.1103/PhysRevLett.119.080401
- PMID 28952755
- Persistent URL
- https://sonar.ch/global/documents/92208
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