Pauli Measurements Are Near-Optimal for Single-Qubit Tomography
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866909711080620032 |
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| author | Acharya, Jayadev Dharmavarapu, Abhilash Liu, Yuhan Yu, Nengkun |
| author_facet | Acharya, Jayadev Dharmavarapu, Abhilash Liu, Yuhan Yu, Nengkun |
| contents | We provide the first non-trivial lower bounds for single-qubit tomography algorithms and show that at least $Ω\left(\frac{10^N}{\sqrt{N} \varepsilon^2}\right)$ copies are required to learn an $N$-qubit state $ρ\in\mathbb{C}^{d\times d},d=2^N$ to within $\varepsilon$ trace distance. Pauli measurements, the most commonly used single-qubit measurement scheme, have recently been shown to require at most $O\left(\frac{10^N}{\varepsilon^2}\right)$ copies for this problem. Combining these results, we nearly settle the long-standing question of the complexity of single-qubit tomography. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_22001 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Pauli Measurements Are Near-Optimal for Single-Qubit Tomography Acharya, Jayadev Dharmavarapu, Abhilash Liu, Yuhan Yu, Nengkun Quantum Physics Computational Complexity We provide the first non-trivial lower bounds for single-qubit tomography algorithms and show that at least $Ω\left(\frac{10^N}{\sqrt{N} \varepsilon^2}\right)$ copies are required to learn an $N$-qubit state $ρ\in\mathbb{C}^{d\times d},d=2^N$ to within $\varepsilon$ trace distance. Pauli measurements, the most commonly used single-qubit measurement scheme, have recently been shown to require at most $O\left(\frac{10^N}{\varepsilon^2}\right)$ copies for this problem. Combining these results, we nearly settle the long-standing question of the complexity of single-qubit tomography. |
| title | Pauli Measurements Are Near-Optimal for Single-Qubit Tomography |
| topic | Quantum Physics Computational Complexity |
| url | https://arxiv.org/abs/2507.22001 |