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arXiv · 2507.22001

Pauli Measurements Are Near-Optimal for Single-Qubit Tomography

Jayadev Acharya·Abhilash Dharmavarapu·Yuhan Liu·Nengkun Yu
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Abstract

We provide the first non-trivial lower bounds for single-qubit tomography algorithms and show that at least ${\Omega}\left(\frac{10^N}{\sqrt{N} \varepsilon^2}\right)$ copies are required to learn an $N$-qubit state $\rho\in\mathbb{C}^{d\times d},d=2^N$ 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.

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Jayadev Acharya, Abhilash Dharmavarapu, Yuhan Liu, Nengkun Yu. 2025-07-29. Pauli Measurements Are Near-Optimal for Single-Qubit Tomography. https://arxiv.org/abs/2507.22001

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