  We investigate the dimensionality of bipartite quantum systems through the
construction of a device-independent null witness test. This test assesses
whether a given bipartite state conforms with the expected quantum dimension,
Schmidt rank, and also distinguishes between real and complex spaces. By
employing local measurements on each party, the proposed method aims to
determine the minimal rank. By performing an experimental demonstration on IBM
Quantum devices, we prove the exceptional accuracy of the test and its
usefulness in diagnostics beyond routine calibrations.
  One of tests shows agreement with theoretical expectations within statistical
errors. However, the second test failed by more than 6 standard deviations,
indicating unspecified parasitic entanglements, with no known simple origin.
