Bounding the quantum dimension with contextuality

Abstract

We show that the phenomenon of quantum contextuality can be used to certify lower bounds on the dimension accessed by the measurement devices. To prove this, we derive bounds for different dimensions and scenarios of the simplest noncontextuality inequalities. The resulting dimension witnesses work independently of the prepared quantum state. Our constructions are robust against noise and imperfections, and we show that a recent experiment can be viewed as an implementation of a state-independent quantum dimension witness.

12 pages, no figures

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• Contextuality in phase space
• Exact dimension estimation of interacting qubit systems assisted by a single quantum probe
• Experimental certification of contextuality, coherence and dimension in a programmable universal photonic processor
• Device-independent certification of Hilbert space dimension using a family of Bell expressions
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• Evidence-based certification of quantum dimensions
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• From the problem of Future Contingents to Peres-Mermin square experiments: An introductory review to Contextuality
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• A State-Dependent Noncontextuality Inequality in Algebraic Quantum Theory
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