Experimental setup with heralded source

In their latest publication in Physical Review Letters, researchers Emil Håkansson, Amelie Piveteau, Alban Seguinard, Sadiq Muhammad, Mohamed Bourennane, and their theory collaborators Otfried Gühne and Martin Plávala present a derivation and experimental implementation of a dimension-dependent contextuality inequality to certify both the quantumness and dimensionality of a given system. Existing methods for certification of the dimension of a quantum system can be cheated by using larger classical systems, creating a potential loophole in these benchmarks, or can only be evaluated in practice, assuming pure quantum states.

"Our approach uses contextuality inequalities that cannot be violated by classical systems, thus closing the previous loopholes. We validate this framework experimentally with photons, observing violations of a CHSH-based contextuality inequality and surpassing the qutrit bound of the CGLMP4-based contextuality inequality. These show that contextuality can be used for noise-robust tests of the number of qubits."

Verifying the fundamental non-classical features of experimental systems

Harnessing the non-classical features of quantum systems has been a central focus of quantum information for decades. These non-classical features have many forms, such as entanglement, Bell nonlocality, or contextuality, and experimental proofs certifying the presence of these non-classical features have significantly impacted our understanding of physics. In order to progress towards practical applications of quantum information, it is necessary not only to experimentally verify the fundamental non-classical features of experimental systems at hand but also to develop meaningful benchmarks that test the quantum devices that are currently available. One of the most basic properties of a quantum computer to benchmark is the number of qubits present in the quantum computer, effectively certifying the dimension of the underlying Hilbert space.

Solving problem in benchmarking quantum devices by closing loopholes

In this work, we develop a novel class of contextuality inequalities that witness the dimension of the underlying quantum system in a prepare-and-measure scenario. Previously developed tests of the dimension of the Hilbert space were plagued by the following loopholes: either passed by a classical system of sufficiently high dimension, or their evaluation in interferometers requires assumptions on the purity. Our approach closes both loopholes: our test cannot be passed by a classical system of an arbitrary high dimension and works for an arbitrary set of preparations, not only for pure states. We thus solve a critical problem in benchmarking quantum devices by closing these loopholes present in previous tests of the dimension of quantum systems.

Experimental setup (See published paper for details, further below) 
The developed contextuality inequalities were also experimentally measured on a Sagnac interferometer, and sufficient violation was observed to certify the dimension of the underlying quantum system. This further demonstrates that the developed inequalities are feasible for certifying the dimension of the Hilbert space in a realistic setup.

The complete study has been published in Physical Review Letters.
Emil Håkansson, Amelie Piveteau, Alban Seguinard, Sadiq Muhammad, Mohamed Bourennane, Otfried Gühne, and Martin Plávala, Phys. Rev. Lett. 134, 200202 (2025), DOI: https://doi.org/10.1103/PhysRevLett.134.200202

More information

Experimental Implementation of Dimension-Dependent Contextuality Inequality | Phys. Rev. Lett.
Physical Review Letters, 2025