Optimal Distributed Similarity Estimation of Quantum Channels

Fuente: arXiv
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Autori principali: Zheng, Congcong, Wang, Kun, Yu, Xutao, Xu, Ping, Zhang, Zaichen
Natura: Preprint
Pubblicazione: 2025
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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