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arXiv · 2605.09958

Quantum Nonlinear Properties from a Single Measurement Setting

Zihao Li·Datong Chen·Dayue Qin·Yuxiang Yang·You Zhou
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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 $\rho$, such as the higher-order expectation value ${\rm tr}(O\rho^t)$ 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.

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Zihao Li, Datong Chen, Dayue Qin, Yuxiang Yang, You Zhou. 2026-05-11. Quantum Nonlinear Properties from a Single Measurement Setting. https://arxiv.org/abs/2605.09958

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