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 $\rho$, 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.

10+45 pages and 9 figures. A new sample complexity lower bound for state moment estimation is added

arXiv:2605.09958 [quant-ph]

(or arXiv:2605.09958v2 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2605.09958 Focus to learn more arXiv-issued DOI via DataCite

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