Quantum Nonlinear Properties from a Single Measurement Setting

• URL: http://arxiv.org/abs/2605.09958v1
• Date: Mon, 11 May 2026 04:12:09 GMT
• Title: Quantum Nonlinear Properties from a Single Measurement Setting
• Abstract summary: We develop a universal framework, collision-based nonlinear estimation (CBNE), for efficiently measuring nonlinear quantities of a quantum state $$.<n>CBNE requires only a single measurement setting, provided that the system dimension is sufficiently large or a few ancillary qubits are available.<n>CBNE is observable-independent at the experimental stage, which enables simultaneous estimation of multiple nonlinear functions.
• Score: 15.153126522080766
• License: http://creativecommons.org/licenses/by/4.0/
• 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 ${\rm tr}(Oρ^t)$ 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.

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