A dimension-independent strict submultiplicativity for the transposition map in diamond norm
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arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866918350150434816 |
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| author | Cha, Hyunho |
| author_facet | Cha, Hyunho |
| contents | We prove that there exists an absolute constant $α<1$ such that for every finite dimension $d$ and every quantum channel $T$ on $\mathsf{L}(\mathbb{C}^d)$, $\left\|Θ\circ(\mathrm{id}-T)\right\|_\diamond \le α\,\left\|Θ\right\|_\diamond\,\left\|\mathrm{id}-T\right\|_\diamond$, where $Θ$ is the transposition map. In fact we show the explicit choice $α=1/\sqrt{2}$ works. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_17748 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A dimension-independent strict submultiplicativity for the transposition map in diamond norm Cha, Hyunho Quantum Physics We prove that there exists an absolute constant $α<1$ such that for every finite dimension $d$ and every quantum channel $T$ on $\mathsf{L}(\mathbb{C}^d)$, $\left\|Θ\circ(\mathrm{id}-T)\right\|_\diamond \le α\,\left\|Θ\right\|_\diamond\,\left\|\mathrm{id}-T\right\|_\diamond$, where $Θ$ is the transposition map. In fact we show the explicit choice $α=1/\sqrt{2}$ works. |
| title | A dimension-independent strict submultiplicativity for the transposition map in diamond norm |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2602.17748 |