Quantum Nonlinear Properties from a Single Measurement Setting
Abstract
Nonlinear properties of quantum states are essential to quantum information and many-body physics, but assessing them experimentally is challenging, as it typically requires multi-copy operations or a large number of measurement settings. To address this challenge, we develop a universal framework, collision-based nonlinear estimation (CBNE), for efficiently measuring nonlinear quantities of a quantum state ρ, such as the higher-order expectation value tr(Oρt) for some observable O, using single-copy randomized measurements. Strikingly, our protocol requires only a single measurement setting, provided that the system dimension is sufficiently large or a few ancillary qubits are available; this contrasts with the conventional expectation that multiple measurement bases are necessary for nonlinear estimation. In addition, CBNE is observable-independent at the experimental stage, which enables simultaneous estimation of multiple nonlinear functions. It further extends to broader tasks, including the estimation of principal component properties and partial-transpose moments of quantum states. Our results provide a practical and scalable route for measuring nonlinear state properties on near-term quantum devices.
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BibTeX
@misc{li2026quantum,
title = {{Quantum Nonlinear Properties from a Single Measurement Setting}},
author = {Zihao Li and Datong Chen and Dayue Qin and Yuxiang Yang and You Zhou},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2605.09958},
eprint = {2605.09958},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.09958},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Quantum Nonlinear Properties from a Single Measurement Setting
AU - Zihao Li
AU - Datong Chen
AU - Dayue Qin
AU - Yuxiang Yang
AU - You Zhou
PY - 2026
DA - 2026/09/30
PB - arXiv
DO - 10.48550/arxiv.2605.09958
UR - https://arxiv.org/abs/2605.09958
AB - Nonlinear properties of quantum states are essential to quantum information and many-body physics, but assessing them experimentally is challenging, as it typically requires multi-copy operations or a large number of measurement settings. To address this challenge, we develop a universal framework, collision-based nonlinear estimation (CBNE), for efficiently measuring nonlinear quantities of a quantum state ρ, such as the higher-order expectation value tr(Oρ^t) for some observable O, using single-copy randomized measurements. Strikingly, our protocol requires only a single measurement setting, provided that the system dimension is sufficiently large or a few ancillary qubits are available; this contrasts with the conventional expectation that multiple measurement bases are necessary for nonlinear estimation. In addition, CBNE is observable-independent at the experimental stage, which enables simultaneous estimation of multiple nonlinear functions. It further extends to broader tasks, including the estimation of principal component properties and partial-transpose moments of quantum states. Our results provide a practical and scalable route for measuring nonlinear state properties on near-term quantum devices.
ER -