Progress on the Kretschmann-Schlingemann-Werner Conjecture
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866910284285739008 |
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| author | Ende, Frederik vom |
| author_facet | Ende, Frederik vom |
| contents | Given any pair of quantum channels $Φ_1,Φ_2$ such that at least one of them has Kraus rank one, as well as any respective Stinespring isometries $V_1,V_2$, we prove that there exists a unitary $U$ on the environment such that $\|V_1-({\bf1}\otimes U)V_2\|_\infty\leq\sqrt{2\|Φ_1-Φ_2\|_\diamond}$. Moreover, we provide a simple example which shows that the factor $\sqrt2$ on the right-hand side is optimal, and we conjecture that this inequality holds for every pair of channels. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_15389 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Progress on the Kretschmann-Schlingemann-Werner Conjecture Ende, Frederik vom Quantum Physics Mathematical Physics Given any pair of quantum channels $Φ_1,Φ_2$ such that at least one of them has Kraus rank one, as well as any respective Stinespring isometries $V_1,V_2$, we prove that there exists a unitary $U$ on the environment such that $\|V_1-({\bf1}\otimes U)V_2\|_\infty\leq\sqrt{2\|Φ_1-Φ_2\|_\diamond}$. Moreover, we provide a simple example which shows that the factor $\sqrt2$ on the right-hand side is optimal, and we conjecture that this inequality holds for every pair of channels. |
| title | Progress on the Kretschmann-Schlingemann-Werner Conjecture |
| topic | Quantum Physics Mathematical Physics |
| url | https://arxiv.org/abs/2308.15389 |