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arXiv · 2307.10727

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

Christopher Popp·Beatrix C. Hiesmayr
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Abstract

Maximally entangled Bell states are of crucial importance for entanglement based methods in quantum information science. Typically, a standard construction of a complete orthonormal Bell-basis by Weyl-Heisenberg operators is considered. We show that the group structure of these operators has strong implication on error correction schemes and on the entanglement structure within Bell-diagonal states. In particular, it implies a equivalence between a Pauli channel and a twirl channel. Interestingly, other complete orthonormal Bell-bases do break the equivalence and lead to a completely different entanglement structure, for instance in the share of PPT-entangled states. In detail, we find that the standard Bell basis has the highest observed share on PPT-states and PPT-entangled states compared to other Bell bases. In summary, our findings show that the standard Bell basis construction exploits a very special structure with strong implications to quantum information theoretic protocols if a deviation is considered.

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Christopher Popp, Beatrix C. Hiesmayr. 2023-07-20. Special features of the Weyl-Heisenberg Bell basis imply unusual entanglement structure of Bell-diagonal states. https://doi.org/10.1088/1367-2630%2Fad1d0e

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