Alejandro Pozas-Kerstjens

We construct and classify entangled measurements with tetrahedral symmetry as group-covariant orbits of a fiducial state. For this class, localizability follows from the Clifford level of a diagonal phase in the fiducial, yielding an explicit hierarchy and efficient constructions. The framework recovers the two-qubit Elegant Joint Measurement (EJM) uniquely and extends it to multiqubit EJMs with identical local geometry but inequivalent global entanglement classes for n\ge3. A continuous family interpolating between the Bell measurement and the EJM realizes an infinite set of localizable tetrahedral bases.