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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2501.11579 |
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| _version_ | 1866912976802414592 |
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| author | Gomez, Jean F. Albrecht, Hermann L. |
| author_facet | Gomez, Jean F. Albrecht, Hermann L. |
| contents | Given the current interest in quantum information tasks involving higher-dimensional systems, we discuss issues that appear when extending the bit-flip channel to qutrit systems. The difficulties arise from the different interpretations of the Pauli X gate for qubits, leading to three inequivalent formulations. We compared our results with the commonly used cyclic one-parameter trit flip channels and demonstrated that they are particular cases of those more general formulations we present here. Also, we extended these channels to higher-dimensional qudit systems, therefore defining different dit flip channels. Finally, we studied their impact on the Negativity, as an entanglement measure, of qubit-qutrit and 2-qutrit Werner states. In doing so, we showed the inequivalence of these versions, as they affect the states' entanglement in very distinct ways. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_11579 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the issues arising when defining an X gate for qudits: Extending the Bit-Flip Channel to $d$-dimensional systems Gomez, Jean F. Albrecht, Hermann L. Quantum Physics Mathematical Physics Given the current interest in quantum information tasks involving higher-dimensional systems, we discuss issues that appear when extending the bit-flip channel to qutrit systems. The difficulties arise from the different interpretations of the Pauli X gate for qubits, leading to three inequivalent formulations. We compared our results with the commonly used cyclic one-parameter trit flip channels and demonstrated that they are particular cases of those more general formulations we present here. Also, we extended these channels to higher-dimensional qudit systems, therefore defining different dit flip channels. Finally, we studied their impact on the Negativity, as an entanglement measure, of qubit-qutrit and 2-qutrit Werner states. In doing so, we showed the inequivalence of these versions, as they affect the states' entanglement in very distinct ways. |
| title | On the issues arising when defining an X gate for qudits: Extending the Bit-Flip Channel to $d$-dimensional systems |
| topic | Quantum Physics Mathematical Physics |
| url | https://arxiv.org/abs/2501.11579 |