Optimal Distributed Similarity Estimation of Quantum Channels
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arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915733729968128 |
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| author | Zheng, Congcong Wang, Kun Yu, Xutao Xu, Ping Zhang, Zaichen |
| author_facet | Zheng, Congcong Wang, Kun Yu, Xutao Xu, Ping Zhang, Zaichen |
| contents | We study distributed similarity estimation of quantum channels (DSEC), a primitive for cross-platform verification where two remote quantum devices are compared by estimating the inner product of their Choi states. We show that the optimal channel query complexity of DSEC for two $d$-dimensional quantum channels is $Θ(\max\{\sqrt{d}/\varepsilon, 1/\varepsilon^2\})$, where $\varepsilon$ is the additive error. We first prove an information-theoretic lower bound with this scaling, which holds even in the strongest setting, allowing adaptive strategies, multiple rounds of classical communication, and coherent access with arbitrary ancillas. We then give a matching upper bound in the weakest setting, namely non-adaptive and ancilla-free incoherent access, via a randomized measurement protocol achieving this bound. Finally, we show that our protocol achieves a quadratic improvement over classical shadow baselines. Our results provide theoretically optimal and practical methods for cross-platform verification, quantum device benchmarking, and distributed quantum learning. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_10465 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Optimal Distributed Similarity Estimation of Quantum Channels Zheng, Congcong Wang, Kun Yu, Xutao Xu, Ping Zhang, Zaichen Quantum Physics We study distributed similarity estimation of quantum channels (DSEC), a primitive for cross-platform verification where two remote quantum devices are compared by estimating the inner product of their Choi states. We show that the optimal channel query complexity of DSEC for two $d$-dimensional quantum channels is $Θ(\max\{\sqrt{d}/\varepsilon, 1/\varepsilon^2\})$, where $\varepsilon$ is the additive error. We first prove an information-theoretic lower bound with this scaling, which holds even in the strongest setting, allowing adaptive strategies, multiple rounds of classical communication, and coherent access with arbitrary ancillas. We then give a matching upper bound in the weakest setting, namely non-adaptive and ancilla-free incoherent access, via a randomized measurement protocol achieving this bound. Finally, we show that our protocol achieves a quadratic improvement over classical shadow baselines. Our results provide theoretically optimal and practical methods for cross-platform verification, quantum device benchmarking, and distributed quantum learning. |
| title | Optimal Distributed Similarity Estimation of Quantum Channels |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2512.10465 |