Special features of the Weyl-Heisenberg Bell basis imply unusual entanglement structure of Bell-diagonal states
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866909077758541824 |
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| author | Popp, Christopher Hiesmayr, Beatrix C. |
| author_facet | Popp, Christopher Hiesmayr, Beatrix C. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_10727 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Special features of the Weyl-Heisenberg Bell basis imply unusual entanglement structure of Bell-diagonal states Popp, Christopher Hiesmayr, Beatrix C. Quantum Physics 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. |
| title | Special features of the Weyl-Heisenberg Bell basis imply unusual entanglement structure of Bell-diagonal states |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2307.10727 |