Singular value transformation for unknown quantum channels
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912482431336448 |
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| author | Niwa, Ryotaro Rossi, Zane Marius Taranto, Philip Murao, Mio |
| author_facet | Niwa, Ryotaro Rossi, Zane Marius Taranto, Philip Murao, Mio |
| contents | Given the ability to apply an unknown quantum channel acting on a $d$-dimensional system, we develop a quantum algorithm for transforming its singular values. The spectrum of a quantum channel as a superoperator is naturally tied to its Liouville representation, which is in general non-Hermitian. Our key contribution is an approximate block-encoding scheme for this representation in a Hermitized form, given only black-box access to the channel; this immediately allows us to apply polynomial transformations to the channel's singular values by quantum singular value transformation (QSVT). We then demonstrate an $O(d^3/δ)$ upper bound and an $Ω(d/δ)$ lower bound for the query complexity of constructing a quantum channel that is $δ$-close in diamond norm to a block-encoding of the Hermitized Liouville representation. We show our method applies practically to the problem of learning the $q$-th singular value moments of unknown quantum channels for arbitrary $q>2, q\in \mathbb{R}$, which has implications for testing if a quantum channel is entanglement breaking. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_24112 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Singular value transformation for unknown quantum channels Niwa, Ryotaro Rossi, Zane Marius Taranto, Philip Murao, Mio Quantum Physics Given the ability to apply an unknown quantum channel acting on a $d$-dimensional system, we develop a quantum algorithm for transforming its singular values. The spectrum of a quantum channel as a superoperator is naturally tied to its Liouville representation, which is in general non-Hermitian. Our key contribution is an approximate block-encoding scheme for this representation in a Hermitized form, given only black-box access to the channel; this immediately allows us to apply polynomial transformations to the channel's singular values by quantum singular value transformation (QSVT). We then demonstrate an $O(d^3/δ)$ upper bound and an $Ω(d/δ)$ lower bound for the query complexity of constructing a quantum channel that is $δ$-close in diamond norm to a block-encoding of the Hermitized Liouville representation. We show our method applies practically to the problem of learning the $q$-th singular value moments of unknown quantum channels for arbitrary $q>2, q\in \mathbb{R}$, which has implications for testing if a quantum channel is entanglement breaking. |
| title | Singular value transformation for unknown quantum channels |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2506.24112 |