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Maximally entangled Bell states are of crucial importance for entanglementbased methods in quantum information science. Typically, a standardconstruction of a complete orthonormal Bell-basis by Weyl-Heisenberg operatorsis considered. We show that the group structure of these operators has strongimplication on error correction schemes and on the entanglement structurewithin Bell-diagonal states. In particular, it implies a equivalence between aPauli channel and a twirl channel. Interestingly, other complete orthonormalBell-bases do break the equivalence and lead to a completely differententanglement structure, for instance in the share of PPT-entangled states. Indetail, we find that the standard Bell basis has the highest observed share onPPT-states and PPT-entangled states compared to other Bell bases. In summary,our findings show that the standard Bell basis construction exploits a veryspecial structure with strong implications to quantum information theoreticprotocols if a deviation is considered.

Special features of the Weyl-Heisenberg Bell basis imply unusual entanglement structure of Bell-diagonal states