Mixed-state additivity properties of magic monotones based on quantum relative entropies for single-qubit states and beyond
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866916495392505856 |
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| author | Rubboli, Roberto Takagi, Ryuji Tomamichel, Marco |
| author_facet | Rubboli, Roberto Takagi, Ryuji Tomamichel, Marco |
| contents | We prove that the stabilizer fidelity is multiplicative for the tensor product of an arbitrary number of single-qubit states. We also show that the relative entropy of magic becomes additive if all the single-qubit states but one belong to a symmetry axis of the stabilizer octahedron. We extend the latter results to include all the $α$-$z$ Rényi relative entropy of magic. This allows us to identify a continuous set of magic monotones that are additive for single-qubit states. We also show that all the monotones mentioned above are additive for several standard two and three-qubit states subject to depolarizing noise. Finally, we obtain closed-form expressions for several states and tighter lower bounds for the overhead of probabilistic one-shot magic state distillation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_08258 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Mixed-state additivity properties of magic monotones based on quantum relative entropies for single-qubit states and beyond Rubboli, Roberto Takagi, Ryuji Tomamichel, Marco Quantum Physics We prove that the stabilizer fidelity is multiplicative for the tensor product of an arbitrary number of single-qubit states. We also show that the relative entropy of magic becomes additive if all the single-qubit states but one belong to a symmetry axis of the stabilizer octahedron. We extend the latter results to include all the $α$-$z$ Rényi relative entropy of magic. This allows us to identify a continuous set of magic monotones that are additive for single-qubit states. We also show that all the monotones mentioned above are additive for several standard two and three-qubit states subject to depolarizing noise. Finally, we obtain closed-form expressions for several states and tighter lower bounds for the overhead of probabilistic one-shot magic state distillation. |
| title | Mixed-state additivity properties of magic monotones based on quantum relative entropies for single-qubit states and beyond |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2307.08258 |