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arXiv · 1611.01258

Witnessing irreducible dimension

Wan Cong·Yu Cai·Jean-Daniel Bancal·Valerio Scarani
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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.

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Wan Cong, Yu Cai, Jean-Daniel Bancal, Valerio Scarani. 2017-08-01. Witnessing irreducible dimension. https://doi.org/10.1103/physrevlett.119.080401

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