Random purification channel made simple
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866910028609355776 |
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| author | Girardi, Filippo Mele, Francesco Anna Lami, Ludovico |
| author_facet | Girardi, Filippo Mele, Francesco Anna Lami, Ludovico |
| contents | The recently introduced random purification channel, which converts $n$ i.i.d. copies of any mixed quantum state into a uniform convex combination of $n$ i.i.d. copies of its purifications, has proved to be an extremely useful tool in quantum learning theory. Here we give a remarkably simple construction of this channel, making its known properties -- and several new ones -- immediately transparent. In particular, we show that the channel also purifies non-i.i.d. states: it transforms any permutationally symmetric state into a uniform convex combination of permutationally symmetric purifications, each differing only by a tensor-product unitary acting on the purifying system. We then apply the channel to give a one-line proof of (a stronger version of) the recently established Uhlmann's theorem for quantum divergences. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_23451 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Random purification channel made simple Girardi, Filippo Mele, Francesco Anna Lami, Ludovico Quantum Physics Other Condensed Matter Mathematical Physics The recently introduced random purification channel, which converts $n$ i.i.d. copies of any mixed quantum state into a uniform convex combination of $n$ i.i.d. copies of its purifications, has proved to be an extremely useful tool in quantum learning theory. Here we give a remarkably simple construction of this channel, making its known properties -- and several new ones -- immediately transparent. In particular, we show that the channel also purifies non-i.i.d. states: it transforms any permutationally symmetric state into a uniform convex combination of permutationally symmetric purifications, each differing only by a tensor-product unitary acting on the purifying system. We then apply the channel to give a one-line proof of (a stronger version of) the recently established Uhlmann's theorem for quantum divergences. |
| title | Random purification channel made simple |
| topic | Quantum Physics Other Condensed Matter Mathematical Physics |
| url | https://arxiv.org/abs/2511.23451 |