Quantum Nonlinear Properties from a Single Measurement Setting
Fuente:
arXiv
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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Acceso en línea: | |
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| _version_ | 1866911670354313216 |
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| author | Li, Zihao Chen, Datong Qin, Dayue Yang, Yuxiang Zhou, You |
| author_facet | Li, Zihao Chen, Datong Qin, Dayue Yang, Yuxiang Zhou, You |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_09958 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Quantum Nonlinear Properties from a Single Measurement Setting Li, Zihao Chen, Datong Qin, Dayue Yang, Yuxiang Zhou, You Quantum Physics 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. |
| title | Quantum Nonlinear Properties from a Single Measurement Setting |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2605.09958 |