Detecting entanglement can be more effective with inequivalent mutually unbiased bases

Abstract Mutually unbiased bases (MUBs) provide a standard tool in the verification of quantum states, especially when harnessing complete set for optimal state tomography. In this work, we investigate detection entanglement via inequivalent sets MUBs, with particular focus on unextendible MUBs. These are which an additional basis cannot be constructed and, consequently, unsuitable verification. Here, show that as well other higher dimensions, can more effective entanglement. Furthermore, efficient and systematic method to search MUBs such occur regularly within Heisenberg–Weyl dimension increases. Our findings particularly useful experimentalists since they demonstrate clever selection allows fewer measurements.