Witnessing Irreducible Dimension
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Updated: Feb 22, 2026

An Operant Intra-/Extra-dimensional Set-shift Task for Mice
Published on: January 22, 2016
Wan Cong1, Yu Cai1, Jean-Daniel Bancal2
1Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543, Singapore.
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 behavior. This dimension can be certified, and we provide a witness for irreducible dimension four.
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