Witnessing irreducible dimension
arXiv:1611.01258 · doi:10.1103/PhysRevLett.119.080401
Abstract
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 behaviour. This dimension can be certified, and we provide a witness for irreducible dimension four.
9 pages, 4 figure
References in corpus (13)
- A convergent hierarchy of semidefinite programs characterizing the set of quantum correlations
- Bounding the set of quantum correlations
- Testing the Hilbert space dimension
- Device-independent tests of classical and quantum dimensions
- All Pure Bipartite Entangled States can be Self-Tested
- Dimension witnesses and quantum state discrimination
- Robust and versatile black-box certification of quantum devices
- Device-independent certification of entangled measurements
- Bounding the set of finite dimensional quantum correlations
- Efficiency of higher dimensional Hilbert spaces for the violation of Bell inequalities
- Robust and stable delay interferometers with application to -dimensional time-frequency quantum key distribution
- A new device-independent dimension witness and its experimental implementation
- Shared randomness and device-independent dimension witnessing
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