Device-independent dimension leakage null test on qubits at low operational cost

We construct a null test of the two-level space of a qubit, which is both device independent and needs a small number of different experiments. We demonstrate its feasibility on IBM Quantum, with most qubits failing the test by more than 10 standard deviations. The robustness of the test against common technical imperfections, like decoherence and phase shifts, and supposedly negligible leakage, indicates that the origin of deviations is beyond known effects.