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Sublinear Copies Suffice for Fidelity Estimation with Pauli Measurements
Abstract
We present the first worst-case, sublinear protocol to estimate the fidelity between a known target state and unknown lab-prepared state using Pauli basis measurements. More precisely, for d-dimensional states, we estimate the fidelity to ± ε using o(d0.9675)/ε2 copies, which applies to all target states. Furthermore, our results establish improved guarantees for Pauli shadow tomography and Distributed Inner Product Estimation.
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BibTeX
@misc{acharya2026sublinear,
title = {{Sublinear Copies Suffice for Fidelity Estimation with Pauli Measurements}},
author = {Jayadev Acharya and Abhilash Dharmavarapu and Yuhan Liu and Nengkun Yu},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.35547},
eprint = {2609.35547},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.35547},
}
RIS
TY - UNPB
TI - Sublinear Copies Suffice for Fidelity Estimation with Pauli Measurements
AU - Jayadev Acharya
AU - Abhilash Dharmavarapu
AU - Yuhan Liu
AU - Nengkun Yu
PY - 2026
DA - 2026/09/28
PB - arXiv
DO - 10.48550/arxiv.2609.35547
UR - https://arxiv.org/abs/2609.35547
AB - We present the first worst-case, sublinear protocol to estimate the fidelity between a known target state and unknown lab-prepared state using Pauli basis measurements. More precisely, for d-dimensional states, we estimate the fidelity to ± ε using o(d^0.9675)/ε^2 copies, which applies to all target states. Furthermore, our results establish improved guarantees for Pauli shadow tomography and Distributed Inner Product Estimation.
ER -